linear_algebra.matrix.nonsingular_inverse ⟷ Mathlib.LinearAlgebra.Matrix.NonsingularInverse

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -589,7 +589,7 @@ theorem inv_zero : (0 : Matrix n n α)⁻¹ = 0 :=
   cases' subsingleton_or_nontrivial α with ht ht
   · simp
   cases' (Fintype.card n).zero_le.eq_or_lt with hc hc
-  · rw [eq_comm, Fintype.card_eq_zero_iff] at hc 
+  · rw [eq_comm, Fintype.card_eq_zero_iff] at hc
     haveI := hc
     ext i
     exact (IsEmpty.false i).elim

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

@@ -3,8 +3,8 @@ Copyright (c) 2019 Tim Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Tim Baanen, Lu-Ming Zhang
 -/
-import Mathbin.Data.Matrix.Invertible
-import Mathbin.LinearAlgebra.Matrix.Adjugate
+import Data.Matrix.Invertible
+import LinearAlgebra.Matrix.Adjugate
 
 #align_import linear_algebra.matrix.nonsingular_inverse from "leanprover-community/mathlib"@"722b3b152ddd5e0cf21c0a29787c76596cb6b422"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504

@@ -77,10 +77,10 @@ variable (A : Matrix n n α) (B : Matrix n n α)
 def invertibleOfDetInvertible [Invertible A.det] : Invertible A
     where
   invOf := ⅟ A.det • A.adjugate
-  mul_invOf_self := by
-    rw [mul_smul_comm, Matrix.mul_eq_mul, mul_adjugate, smul_smul, invOf_mul_self, one_smul]
-  invOf_mul_self := by
-    rw [smul_mul_assoc, Matrix.mul_eq_mul, adjugate_mul, smul_smul, invOf_mul_self, one_smul]
+  hMul_invOf_self := by
+    rw [mul_smul_comm, Matrix.hMul_eq_hMul, mul_adjugate, smul_smul, invOf_mul_self, one_smul]
+  invOf_hMul_self := by
+    rw [smul_mul_assoc, Matrix.hMul_eq_hMul, adjugate_mul, smul_smul, invOf_mul_self, one_smul]
 #align matrix.invertible_of_det_invertible Matrix.invertibleOfDetInvertible
 -/
 
@@ -95,8 +95,8 @@ theorem invOf_eq [Invertible A.det] [Invertible A] : ⅟ A = ⅟ A.det • A.adj
 def detInvertibleOfLeftInverse (h : B ⬝ A = 1) : Invertible A.det
     where
   invOf := B.det
-  mul_invOf_self := by rw [mul_comm, ← det_mul, h, det_one]
-  invOf_mul_self := by rw [← det_mul, h, det_one]
+  hMul_invOf_self := by rw [mul_comm, ← det_mul, h, det_one]
+  invOf_hMul_self := by rw [← det_mul, h, det_one]
 #align matrix.det_invertible_of_left_inverse Matrix.detInvertibleOfLeftInverse
 -/
 
@@ -105,8 +105,8 @@ def detInvertibleOfLeftInverse (h : B ⬝ A = 1) : Invertible A.det
 def detInvertibleOfRightInverse (h : A ⬝ B = 1) : Invertible A.det
     where
   invOf := B.det
-  mul_invOf_self := by rw [← det_mul, h, det_one]
-  invOf_mul_self := by rw [mul_comm, ← det_mul, h, det_one]
+  hMul_invOf_self := by rw [← det_mul, h, det_one]
+  invOf_hMul_self := by rw [mul_comm, ← det_mul, h, det_one]
 #align matrix.det_invertible_of_right_inverse Matrix.detInvertibleOfRightInverse
 -/
 
@@ -145,10 +145,10 @@ theorem mul_eq_one_comm : A ⬝ B = 1 ↔ B ⬝ A = 1 :=
   letI : Invertible B.det := det_invertible_of_left_inverse _ _ h
   letI : Invertible B := invertible_of_det_invertible B
   calc
-    B ⬝ A = B ⬝ A ⬝ (B ⬝ ⅟ B) := by rw [Matrix.mul_invOf_self, Matrix.mul_one]
+    B ⬝ A = B ⬝ A ⬝ (B ⬝ ⅟ B) := by rw [mul_invOf_self, Matrix.mul_one]
     _ = B ⬝ (A ⬝ B ⬝ ⅟ B) := by simp only [Matrix.mul_assoc]
     _ = B ⬝ ⅟ B := by rw [h, Matrix.one_mul]
-    _ = 1 := Matrix.mul_invOf_self B
+    _ = 1 := mul_invOf_self B
 #align matrix.mul_eq_one_comm Matrix.mul_eq_one_comm
 -/
 
@@ -343,7 +343,7 @@ theorem conjTranspose_nonsing_inv [StarRing α] : A⁻¹ᴴ = Aᴴ⁻¹ := by
 theorem mul_nonsing_inv (h : IsUnit A.det) : A ⬝ A⁻¹ = 1 :=
   by
   cases (A.is_unit_iff_is_unit_det.mpr h).nonempty_invertible
-  rw [← inv_of_eq_nonsing_inv, Matrix.mul_invOf_self]
+  rw [← inv_of_eq_nonsing_inv, mul_invOf_self]
 #align matrix.mul_nonsing_inv Matrix.mul_nonsing_inv
 -/
 
@@ -353,7 +353,7 @@ theorem mul_nonsing_inv (h : IsUnit A.det) : A ⬝ A⁻¹ = 1 :=
 theorem nonsing_inv_mul (h : IsUnit A.det) : A⁻¹ ⬝ A = 1 :=
   by
   cases (A.is_unit_iff_is_unit_det.mpr h).nonempty_invertible
-  rw [← inv_of_eq_nonsing_inv, Matrix.invOf_mul_self]
+  rw [← inv_of_eq_nonsing_inv, invOf_mul_self]
 #align matrix.nonsing_inv_mul Matrix.nonsing_inv_mul
 -/
 
@@ -647,7 +647,7 @@ theorem invOf_diagonal_eq {α} [Semiring α] (v : n → α) [Invertible v] [Inve
 def invertibleOfDiagonalInvertible (v : n → α) [Invertible (diagonal v)] : Invertible v
     where
   invOf := diag (⅟ (diagonal v))
-  invOf_mul_self :=
+  invOf_hMul_self :=
     funext fun i =>
       by
       letI : Invertible (diagonal v).det := det_invertible_of_invertible _
@@ -655,7 +655,7 @@ def invertibleOfDiagonalInvertible (v : n → α) [Invertible (diagonal v)] : In
       dsimp
       rw [mul_assoc, prod_erase_mul _ _ (Finset.mem_univ _), ← det_diagonal]
       exact mul_invOf_self _
-  mul_invOf_self :=
+  hMul_invOf_self :=
     funext fun i =>
       by
       letI : Invertible (diagonal v).det := det_invertible_of_invertible _
@@ -729,8 +729,8 @@ theorem mul_inv_rev (A B : Matrix n n α) : (A ⬝ B)⁻¹ = B⁻¹ ⬝ A⁻¹ :
 theorem list_prod_inv_reverse : ∀ l : List (Matrix n n α), l.Prod⁻¹ = (l.reverse.map Inv.inv).Prod
   | [] => by rw [List.reverse_nil, List.map_nil, List.prod_nil, inv_one]
   | A::Xs => by
-    rw [List.reverse_cons', List.map_concat, List.prod_concat, List.prod_cons, Matrix.mul_eq_mul,
-      Matrix.mul_eq_mul, mul_inv_rev, list_prod_inv_reverse]
+    rw [List.reverse_cons', List.map_concat, List.prod_concat, List.prod_cons, Matrix.hMul_eq_hMul,
+      Matrix.hMul_eq_hMul, mul_inv_rev, list_prod_inv_reverse]
 #align matrix.list_prod_inv_reverse Matrix.list_prod_inv_reverse
 -/
 
@@ -772,7 +772,7 @@ variable [DecidableEq m]
 def submatrixEquivInvertible (A : Matrix m m α) (e₁ e₂ : n ≃ m) [Invertible A] :
     Invertible (A.submatrix e₁ e₂) :=
   invertibleOfRightInverse _ ((⅟ A).submatrix e₂ e₁) <| by
-    rw [Matrix.submatrix_mul_equiv, Matrix.mul_invOf_self, submatrix_one_equiv]
+    rw [Matrix.submatrix_mul_equiv, mul_invOf_self, submatrix_one_equiv]
 #align matrix.submatrix_equiv_invertible Matrix.submatrixEquivInvertible
 -/
 
@@ -786,7 +786,7 @@ def invertibleOfSubmatrixEquivInvertible (A : Matrix m m α) (e₁ e₂ : n ≃
     conv in _ ⬝ _ =>
       congr
       rw [this]
-    rw [Matrix.submatrix_mul_equiv, Matrix.mul_invOf_self, submatrix_one_equiv]
+    rw [Matrix.submatrix_mul_equiv, mul_invOf_self, submatrix_one_equiv]
 #align matrix.invertible_of_submatrix_equiv_invertible Matrix.invertibleOfSubmatrixEquivInvertible
 -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

@@ -2,15 +2,12 @@
 Copyright (c) 2019 Tim Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Tim Baanen, Lu-Ming Zhang
-
-! This file was ported from Lean 3 source module linear_algebra.matrix.nonsingular_inverse
-! leanprover-community/mathlib commit 722b3b152ddd5e0cf21c0a29787c76596cb6b422
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Matrix.Invertible
 import Mathbin.LinearAlgebra.Matrix.Adjugate
 
+#align_import linear_algebra.matrix.nonsingular_inverse from "leanprover-community/mathlib"@"722b3b152ddd5e0cf21c0a29787c76596cb6b422"
+
 /-!
 # Nonsingular inverses
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/6285167a053ad0990fc88e56c48ccd9fae6550eb

@@ -4,10 +4,11 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Tim Baanen, Lu-Ming Zhang
 
 ! This file was ported from Lean 3 source module linear_algebra.matrix.nonsingular_inverse
-! leanprover-community/mathlib commit 9d2f0748e6c50d7a2657c564b1ff2c695b39148d
+! leanprover-community/mathlib commit 722b3b152ddd5e0cf21c0a29787c76596cb6b422
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
+import Mathbin.Data.Matrix.Invertible
 import Mathbin.LinearAlgebra.Matrix.Adjugate
 
 /-!
@@ -72,48 +73,6 @@ section Invertible
 
 variable [Fintype n] [DecidableEq n] [CommRing α]
 
-#print Matrix.invOf_mul_self /-
-/-- A copy of `inv_of_mul_self` using `⬝` not `*`. -/
-protected theorem invOf_mul_self (A : Matrix n n α) [Invertible A] : ⅟ A ⬝ A = 1 :=
-  invOf_mul_self A
-#align matrix.inv_of_mul_self Matrix.invOf_mul_self
--/
-
-#print Matrix.mul_invOf_self /-
-/-- A copy of `mul_inv_of_self` using `⬝` not `*`. -/
-protected theorem mul_invOf_self (A : Matrix n n α) [Invertible A] : A ⬝ ⅟ A = 1 :=
-  mul_invOf_self A
-#align matrix.mul_inv_of_self Matrix.mul_invOf_self
--/
-
-#print Matrix.invOf_mul_self_assoc /-
-/-- A copy of `inv_of_mul_self_assoc` using `⬝` not `*`. -/
-protected theorem invOf_mul_self_assoc (A : Matrix n n α) (B : Matrix n m α) [Invertible A] :
-    ⅟ A ⬝ (A ⬝ B) = B := by rw [← Matrix.mul_assoc, Matrix.invOf_mul_self, Matrix.one_mul]
-#align matrix.inv_of_mul_self_assoc Matrix.invOf_mul_self_assoc
--/
-
-#print Matrix.mul_invOf_self_assoc /-
-/-- A copy of `mul_inv_of_self_assoc` using `⬝` not `*`. -/
-protected theorem mul_invOf_self_assoc (A : Matrix n n α) (B : Matrix n m α) [Invertible A] :
-    A ⬝ (⅟ A ⬝ B) = B := by rw [← Matrix.mul_assoc, Matrix.mul_invOf_self, Matrix.one_mul]
-#align matrix.mul_inv_of_self_assoc Matrix.mul_invOf_self_assoc
--/
-
-#print Matrix.mul_invOf_mul_self_cancel /-
-/-- A copy of `mul_inv_of_mul_self_cancel` using `⬝` not `*`. -/
-protected theorem mul_invOf_mul_self_cancel (A : Matrix m n α) (B : Matrix n n α) [Invertible B] :
-    A ⬝ ⅟ B ⬝ B = A := by rw [Matrix.mul_assoc, Matrix.invOf_mul_self, Matrix.mul_one]
-#align matrix.mul_inv_of_mul_self_cancel Matrix.mul_invOf_mul_self_cancel
--/
-
-#print Matrix.mul_mul_invOf_self_cancel /-
-/-- A copy of `mul_mul_inv_of_self_cancel` using `⬝` not `*`. -/
-protected theorem mul_mul_invOf_self_cancel (A : Matrix m n α) (B : Matrix n n α) [Invertible B] :
-    A ⬝ B ⬝ ⅟ B = A := by rw [Matrix.mul_assoc, Matrix.mul_invOf_self, Matrix.mul_one]
-#align matrix.mul_mul_inv_of_self_cancel Matrix.mul_mul_invOf_self_cancel
--/
-
 variable (A : Matrix n n α) (B : Matrix n n α)
 
 #print Matrix.invertibleOfDetInvertible /-

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

@@ -72,38 +72,51 @@ section Invertible
 
 variable [Fintype n] [DecidableEq n] [CommRing α]
 
+#print Matrix.invOf_mul_self /-
 /-- A copy of `inv_of_mul_self` using `⬝` not `*`. -/
 protected theorem invOf_mul_self (A : Matrix n n α) [Invertible A] : ⅟ A ⬝ A = 1 :=
   invOf_mul_self A
 #align matrix.inv_of_mul_self Matrix.invOf_mul_self
+-/
 
+#print Matrix.mul_invOf_self /-
 /-- A copy of `mul_inv_of_self` using `⬝` not `*`. -/
 protected theorem mul_invOf_self (A : Matrix n n α) [Invertible A] : A ⬝ ⅟ A = 1 :=
   mul_invOf_self A
 #align matrix.mul_inv_of_self Matrix.mul_invOf_self
+-/
 
+#print Matrix.invOf_mul_self_assoc /-
 /-- A copy of `inv_of_mul_self_assoc` using `⬝` not `*`. -/
 protected theorem invOf_mul_self_assoc (A : Matrix n n α) (B : Matrix n m α) [Invertible A] :
     ⅟ A ⬝ (A ⬝ B) = B := by rw [← Matrix.mul_assoc, Matrix.invOf_mul_self, Matrix.one_mul]
 #align matrix.inv_of_mul_self_assoc Matrix.invOf_mul_self_assoc
+-/
 
+#print Matrix.mul_invOf_self_assoc /-
 /-- A copy of `mul_inv_of_self_assoc` using `⬝` not `*`. -/
 protected theorem mul_invOf_self_assoc (A : Matrix n n α) (B : Matrix n m α) [Invertible A] :
     A ⬝ (⅟ A ⬝ B) = B := by rw [← Matrix.mul_assoc, Matrix.mul_invOf_self, Matrix.one_mul]
 #align matrix.mul_inv_of_self_assoc Matrix.mul_invOf_self_assoc
+-/
 
+#print Matrix.mul_invOf_mul_self_cancel /-
 /-- A copy of `mul_inv_of_mul_self_cancel` using `⬝` not `*`. -/
 protected theorem mul_invOf_mul_self_cancel (A : Matrix m n α) (B : Matrix n n α) [Invertible B] :
     A ⬝ ⅟ B ⬝ B = A := by rw [Matrix.mul_assoc, Matrix.invOf_mul_self, Matrix.mul_one]
 #align matrix.mul_inv_of_mul_self_cancel Matrix.mul_invOf_mul_self_cancel
+-/
 
+#print Matrix.mul_mul_invOf_self_cancel /-
 /-- A copy of `mul_mul_inv_of_self_cancel` using `⬝` not `*`. -/
 protected theorem mul_mul_invOf_self_cancel (A : Matrix m n α) (B : Matrix n n α) [Invertible B] :
     A ⬝ B ⬝ ⅟ B = A := by rw [Matrix.mul_assoc, Matrix.mul_invOf_self, Matrix.mul_one]
 #align matrix.mul_mul_inv_of_self_cancel Matrix.mul_mul_invOf_self_cancel
+-/
 
 variable (A : Matrix n n α) (B : Matrix n n α)
 
+#print Matrix.invertibleOfDetInvertible /-
 /-- If `A.det` has a constructive inverse, produce one for `A`. -/
 def invertibleOfDetInvertible [Invertible A.det] : Invertible A
     where
@@ -113,11 +126,15 @@ def invertibleOfDetInvertible [Invertible A.det] : Invertible A
   invOf_mul_self := by
     rw [smul_mul_assoc, Matrix.mul_eq_mul, adjugate_mul, smul_smul, invOf_mul_self, one_smul]
 #align matrix.invertible_of_det_invertible Matrix.invertibleOfDetInvertible
+-/
 
+#print Matrix.invOf_eq /-
 theorem invOf_eq [Invertible A.det] [Invertible A] : ⅟ A = ⅟ A.det • A.adjugate := by
   letI := invertible_of_det_invertible A; convert (rfl : ⅟ A = _)
 #align matrix.inv_of_eq Matrix.invOf_eq
+-/
 
+#print Matrix.detInvertibleOfLeftInverse /-
 /-- `A.det` is invertible if `A` has a left inverse. -/
 def detInvertibleOfLeftInverse (h : B ⬝ A = 1) : Invertible A.det
     where
@@ -125,7 +142,9 @@ def detInvertibleOfLeftInverse (h : B ⬝ A = 1) : Invertible A.det
   mul_invOf_self := by rw [mul_comm, ← det_mul, h, det_one]
   invOf_mul_self := by rw [← det_mul, h, det_one]
 #align matrix.det_invertible_of_left_inverse Matrix.detInvertibleOfLeftInverse
+-/
 
+#print Matrix.detInvertibleOfRightInverse /-
 /-- `A.det` is invertible if `A` has a right inverse. -/
 def detInvertibleOfRightInverse (h : A ⬝ B = 1) : Invertible A.det
     where
@@ -133,16 +152,22 @@ def detInvertibleOfRightInverse (h : A ⬝ B = 1) : Invertible A.det
   mul_invOf_self := by rw [← det_mul, h, det_one]
   invOf_mul_self := by rw [mul_comm, ← det_mul, h, det_one]
 #align matrix.det_invertible_of_right_inverse Matrix.detInvertibleOfRightInverse
+-/
 
+#print Matrix.detInvertibleOfInvertible /-
 /-- If `A` has a constructive inverse, produce one for `A.det`. -/
 def detInvertibleOfInvertible [Invertible A] : Invertible A.det :=
   detInvertibleOfLeftInverse A (⅟ A) (invOf_mul_self _)
 #align matrix.det_invertible_of_invertible Matrix.detInvertibleOfInvertible
+-/
 
+#print Matrix.det_invOf /-
 theorem det_invOf [Invertible A] [Invertible A.det] : (⅟ A).det = ⅟ A.det := by
   letI := det_invertible_of_invertible A; convert (rfl : _ = ⅟ A.det)
 #align matrix.det_inv_of Matrix.det_invOf
+-/
 
+#print Matrix.invertibleEquivDetInvertible /-
 /-- Together `matrix.det_invertible_of_invertible` and `matrix.invertible_of_det_invertible` form an
 equivalence, although both sides of the equiv are subsingleton anyway. -/
 @[simps]
@@ -153,9 +178,11 @@ def invertibleEquivDetInvertible : Invertible A ≃ Invertible A.det
   left_inv _ := Subsingleton.elim _ _
   right_inv _ := Subsingleton.elim _ _
 #align matrix.invertible_equiv_det_invertible Matrix.invertibleEquivDetInvertible
+-/
 
 variable {A B}
 
+#print Matrix.mul_eq_one_comm /-
 theorem mul_eq_one_comm : A ⬝ B = 1 ↔ B ⬝ A = 1 :=
   suffices ∀ A B, A ⬝ B = 1 → B ⬝ A = 1 from ⟨this A B, this B A⟩
   fun A B h => by
@@ -167,81 +194,110 @@ theorem mul_eq_one_comm : A ⬝ B = 1 ↔ B ⬝ A = 1 :=
     _ = B ⬝ ⅟ B := by rw [h, Matrix.one_mul]
     _ = 1 := Matrix.mul_invOf_self B
 #align matrix.mul_eq_one_comm Matrix.mul_eq_one_comm
+-/
 
 variable (A B)
 
+#print Matrix.invertibleOfLeftInverse /-
 /-- We can construct an instance of invertible A if A has a left inverse. -/
 def invertibleOfLeftInverse (h : B ⬝ A = 1) : Invertible A :=
   ⟨B, h, mul_eq_one_comm.mp h⟩
 #align matrix.invertible_of_left_inverse Matrix.invertibleOfLeftInverse
+-/
 
+#print Matrix.invertibleOfRightInverse /-
 /-- We can construct an instance of invertible A if A has a right inverse. -/
 def invertibleOfRightInverse (h : A ⬝ B = 1) : Invertible A :=
   ⟨B, mul_eq_one_comm.mp h, h⟩
 #align matrix.invertible_of_right_inverse Matrix.invertibleOfRightInverse
+-/
 
+#print Matrix.invertibleTranspose /-
 /-- The transpose of an invertible matrix is invertible. -/
 instance invertibleTranspose [Invertible A] : Invertible Aᵀ :=
   haveI : Invertible Aᵀ.det := by simpa using det_invertible_of_invertible A
   invertible_of_det_invertible Aᵀ
 #align matrix.invertible_transpose Matrix.invertibleTranspose
+-/
 
+#print Matrix.invertibleOfInvertibleTranspose /-
 /-- A matrix is invertible if the transpose is invertible. -/
 def invertibleOfInvertibleTranspose [Invertible Aᵀ] : Invertible A :=
   by
   rw [← transpose_transpose A]
   infer_instance
 #align matrix.invertible__of_invertible_transpose Matrix.invertibleOfInvertibleTranspose
+-/
 
+#print Matrix.invertibleOfInvertibleConjTranspose /-
 /-- A matrix is invertible if the conjugate transpose is invertible. -/
 def invertibleOfInvertibleConjTranspose [StarRing α] [Invertible Aᴴ] : Invertible A :=
   by
   rw [← conj_transpose_conj_transpose A]
   infer_instance
 #align matrix.invertible_of_invertible_conj_transpose Matrix.invertibleOfInvertibleConjTranspose
+-/
 
+#print Matrix.unitOfDetInvertible /-
 /-- Given a proof that `A.det` has a constructive inverse, lift `A` to `(matrix n n α)ˣ`-/
 def unitOfDetInvertible [Invertible A.det] : (Matrix n n α)ˣ :=
   @unitOfInvertible _ _ A (invertibleOfDetInvertible A)
 #align matrix.unit_of_det_invertible Matrix.unitOfDetInvertible
+-/
 
+#print Matrix.isUnit_iff_isUnit_det /-
 /-- When lowered to a prop, `matrix.invertible_equiv_det_invertible` forms an `iff`. -/
 theorem isUnit_iff_isUnit_det : IsUnit A ↔ IsUnit A.det := by
   simp only [← nonempty_invertible_iff_isUnit, (invertible_equiv_det_invertible A).nonempty_congr]
 #align matrix.is_unit_iff_is_unit_det Matrix.isUnit_iff_isUnit_det
+-/
 
 /-! #### Variants of the statements above with `is_unit`-/
 
 
+#print Matrix.isUnit_det_of_invertible /-
 theorem isUnit_det_of_invertible [Invertible A] : IsUnit A.det :=
   @isUnit_of_invertible _ _ _ (detInvertibleOfInvertible A)
 #align matrix.is_unit_det_of_invertible Matrix.isUnit_det_of_invertible
+-/
 
 variable {A B}
 
+#print Matrix.isUnit_of_left_inverse /-
 theorem isUnit_of_left_inverse (h : B ⬝ A = 1) : IsUnit A :=
   ⟨⟨A, B, mul_eq_one_comm.mp h, h⟩, rfl⟩
 #align matrix.is_unit_of_left_inverse Matrix.isUnit_of_left_inverse
+-/
 
+#print Matrix.isUnit_of_right_inverse /-
 theorem isUnit_of_right_inverse (h : A ⬝ B = 1) : IsUnit A :=
   ⟨⟨A, B, h, mul_eq_one_comm.mp h⟩, rfl⟩
 #align matrix.is_unit_of_right_inverse Matrix.isUnit_of_right_inverse
+-/
 
+#print Matrix.isUnit_det_of_left_inverse /-
 theorem isUnit_det_of_left_inverse (h : B ⬝ A = 1) : IsUnit A.det :=
   @isUnit_of_invertible _ _ _ (detInvertibleOfLeftInverse _ _ h)
 #align matrix.is_unit_det_of_left_inverse Matrix.isUnit_det_of_left_inverse
+-/
 
+#print Matrix.isUnit_det_of_right_inverse /-
 theorem isUnit_det_of_right_inverse (h : A ⬝ B = 1) : IsUnit A.det :=
   @isUnit_of_invertible _ _ _ (detInvertibleOfRightInverse _ _ h)
 #align matrix.is_unit_det_of_right_inverse Matrix.isUnit_det_of_right_inverse
+-/
 
+#print Matrix.det_ne_zero_of_left_inverse /-
 theorem det_ne_zero_of_left_inverse [Nontrivial α] (h : B ⬝ A = 1) : A.det ≠ 0 :=
   (isUnit_det_of_left_inverse h).NeZero
 #align matrix.det_ne_zero_of_left_inverse Matrix.det_ne_zero_of_left_inverse
+-/
 
+#print Matrix.det_ne_zero_of_right_inverse /-
 theorem det_ne_zero_of_right_inverse [Nontrivial α] (h : A ⬝ B = 1) : A.det ≠ 0 :=
   (isUnit_det_of_right_inverse h).NeZero
 #align matrix.det_ne_zero_of_right_inverse Matrix.det_ne_zero_of_right_inverse
+-/
 
 end Invertible
 
@@ -249,8 +305,10 @@ variable [Fintype n] [DecidableEq n] [CommRing α]
 
 variable (A : Matrix n n α) (B : Matrix n n α)
 
+#print Matrix.isUnit_det_transpose /-
 theorem isUnit_det_transpose (h : IsUnit A.det) : IsUnit Aᵀ.det := by rw [det_transpose]; exact h
 #align matrix.is_unit_det_transpose Matrix.isUnit_det_transpose
+-/
 
 /-! ### A noncomputable `has_inv` instance  -/
 
@@ -259,18 +317,25 @@ theorem isUnit_det_transpose (h : IsUnit A.det) : IsUnit Aᵀ.det := by rw [det_
 noncomputable instance : Inv (Matrix n n α) :=
   ⟨fun A => Ring.inverse A.det • A.adjugate⟩
 
+#print Matrix.inv_def /-
 theorem inv_def (A : Matrix n n α) : A⁻¹ = Ring.inverse A.det • A.adjugate :=
   rfl
 #align matrix.inv_def Matrix.inv_def
+-/
 
+#print Matrix.nonsing_inv_apply_not_isUnit /-
 theorem nonsing_inv_apply_not_isUnit (h : ¬IsUnit A.det) : A⁻¹ = 0 := by
   rw [inv_def, Ring.inverse_non_unit _ h, zero_smul]
 #align matrix.nonsing_inv_apply_not_is_unit Matrix.nonsing_inv_apply_not_isUnit
+-/
 
+#print Matrix.nonsing_inv_apply /-
 theorem nonsing_inv_apply (h : IsUnit A.det) : A⁻¹ = (↑h.Unit⁻¹ : α) • A.adjugate := by
   rw [inv_def, ← Ring.inverse_unit h.unit, IsUnit.unit_spec]
 #align matrix.nonsing_inv_apply Matrix.nonsing_inv_apply
+-/
 
+#print Matrix.invOf_eq_nonsing_inv /-
 /-- The nonsingular inverse is the same as `inv_of` when `A` is invertible. -/
 @[simp]
 theorem invOf_eq_nonsing_inv [Invertible A] : ⅟ A = A⁻¹ :=
@@ -278,7 +343,9 @@ theorem invOf_eq_nonsing_inv [Invertible A] : ⅟ A = A⁻¹ :=
   letI := det_invertible_of_invertible A
   rw [inv_def, Ring.inverse_invertible, inv_of_eq]
 #align matrix.inv_of_eq_nonsing_inv Matrix.invOf_eq_nonsing_inv
+-/
 
+#print Matrix.coe_units_inv /-
 /-- Coercing the result of `units.has_inv` is the same as coercing first and applying the
 nonsingular inverse. -/
 @[simp, norm_cast]
@@ -287,7 +354,9 @@ theorem coe_units_inv (A : (Matrix n n α)ˣ) : ↑A⁻¹ = (A⁻¹ : Matrix n n
   letI := A.invertible
   rw [← inv_of_eq_nonsing_inv, invOf_units]
 #align matrix.coe_units_inv Matrix.coe_units_inv
+-/
 
+#print Matrix.nonsing_inv_eq_ring_inverse /-
 /-- The nonsingular inverse is the same as the general `ring.inverse`. -/
 theorem nonsing_inv_eq_ring_inverse : A⁻¹ = Ring.inverse A :=
   by
@@ -297,16 +366,22 @@ theorem nonsing_inv_eq_ring_inverse : A⁻¹ = Ring.inverse A :=
   · have h := mt A.is_unit_iff_is_unit_det.mp h_det
     rw [Ring.inverse_non_unit _ h, nonsing_inv_apply_not_is_unit A h_det]
 #align matrix.nonsing_inv_eq_ring_inverse Matrix.nonsing_inv_eq_ring_inverse
+-/
 
+#print Matrix.transpose_nonsing_inv /-
 theorem transpose_nonsing_inv : A⁻¹ᵀ = Aᵀ⁻¹ := by
   rw [inv_def, inv_def, transpose_smul, det_transpose, adjugate_transpose]
 #align matrix.transpose_nonsing_inv Matrix.transpose_nonsing_inv
+-/
 
+#print Matrix.conjTranspose_nonsing_inv /-
 theorem conjTranspose_nonsing_inv [StarRing α] : A⁻¹ᴴ = Aᴴ⁻¹ := by
   rw [inv_def, inv_def, conj_transpose_smul, det_conj_transpose, adjugate_conj_transpose,
     Ring.inverse_star]
 #align matrix.conj_transpose_nonsing_inv Matrix.conjTranspose_nonsing_inv
+-/
 
+#print Matrix.mul_nonsing_inv /-
 /-- The `nonsing_inv` of `A` is a right inverse. -/
 @[simp]
 theorem mul_nonsing_inv (h : IsUnit A.det) : A ⬝ A⁻¹ = 1 :=
@@ -314,7 +389,9 @@ theorem mul_nonsing_inv (h : IsUnit A.det) : A ⬝ A⁻¹ = 1 :=
   cases (A.is_unit_iff_is_unit_det.mpr h).nonempty_invertible
   rw [← inv_of_eq_nonsing_inv, Matrix.mul_invOf_self]
 #align matrix.mul_nonsing_inv Matrix.mul_nonsing_inv
+-/
 
+#print Matrix.nonsing_inv_mul /-
 /-- The `nonsing_inv` of `A` is a left inverse. -/
 @[simp]
 theorem nonsing_inv_mul (h : IsUnit A.det) : A⁻¹ ⬝ A = 1 :=
@@ -322,87 +399,119 @@ theorem nonsing_inv_mul (h : IsUnit A.det) : A⁻¹ ⬝ A = 1 :=
   cases (A.is_unit_iff_is_unit_det.mpr h).nonempty_invertible
   rw [← inv_of_eq_nonsing_inv, Matrix.invOf_mul_self]
 #align matrix.nonsing_inv_mul Matrix.nonsing_inv_mul
+-/
 
 instance [Invertible A] : Invertible A⁻¹ := by rw [← inv_of_eq_nonsing_inv]; infer_instance
 
+#print Matrix.inv_inv_of_invertible /-
 @[simp]
 theorem inv_inv_of_invertible [Invertible A] : A⁻¹⁻¹ = A := by
   simp only [← inv_of_eq_nonsing_inv, invOf_invOf]
 #align matrix.inv_inv_of_invertible Matrix.inv_inv_of_invertible
+-/
 
+#print Matrix.mul_nonsing_inv_cancel_right /-
 @[simp]
 theorem mul_nonsing_inv_cancel_right (B : Matrix m n α) (h : IsUnit A.det) : B ⬝ A ⬝ A⁻¹ = B := by
   simp [Matrix.mul_assoc, mul_nonsing_inv A h]
 #align matrix.mul_nonsing_inv_cancel_right Matrix.mul_nonsing_inv_cancel_right
+-/
 
+#print Matrix.mul_nonsing_inv_cancel_left /-
 @[simp]
 theorem mul_nonsing_inv_cancel_left (B : Matrix n m α) (h : IsUnit A.det) : A ⬝ (A⁻¹ ⬝ B) = B := by
   simp [← Matrix.mul_assoc, mul_nonsing_inv A h]
 #align matrix.mul_nonsing_inv_cancel_left Matrix.mul_nonsing_inv_cancel_left
+-/
 
+#print Matrix.nonsing_inv_mul_cancel_right /-
 @[simp]
 theorem nonsing_inv_mul_cancel_right (B : Matrix m n α) (h : IsUnit A.det) : B ⬝ A⁻¹ ⬝ A = B := by
   simp [Matrix.mul_assoc, nonsing_inv_mul A h]
 #align matrix.nonsing_inv_mul_cancel_right Matrix.nonsing_inv_mul_cancel_right
+-/
 
+#print Matrix.nonsing_inv_mul_cancel_left /-
 @[simp]
 theorem nonsing_inv_mul_cancel_left (B : Matrix n m α) (h : IsUnit A.det) : A⁻¹ ⬝ (A ⬝ B) = B := by
   simp [← Matrix.mul_assoc, nonsing_inv_mul A h]
 #align matrix.nonsing_inv_mul_cancel_left Matrix.nonsing_inv_mul_cancel_left
+-/
 
+#print Matrix.mul_inv_of_invertible /-
 @[simp]
 theorem mul_inv_of_invertible [Invertible A] : A ⬝ A⁻¹ = 1 :=
   mul_nonsing_inv A (isUnit_det_of_invertible A)
 #align matrix.mul_inv_of_invertible Matrix.mul_inv_of_invertible
+-/
 
+#print Matrix.inv_mul_of_invertible /-
 @[simp]
 theorem inv_mul_of_invertible [Invertible A] : A⁻¹ ⬝ A = 1 :=
   nonsing_inv_mul A (isUnit_det_of_invertible A)
 #align matrix.inv_mul_of_invertible Matrix.inv_mul_of_invertible
+-/
 
+#print Matrix.mul_inv_cancel_right_of_invertible /-
 @[simp]
 theorem mul_inv_cancel_right_of_invertible (B : Matrix m n α) [Invertible A] : B ⬝ A ⬝ A⁻¹ = B :=
   mul_nonsing_inv_cancel_right A B (isUnit_det_of_invertible A)
 #align matrix.mul_inv_cancel_right_of_invertible Matrix.mul_inv_cancel_right_of_invertible
+-/
 
+#print Matrix.mul_inv_cancel_left_of_invertible /-
 @[simp]
 theorem mul_inv_cancel_left_of_invertible (B : Matrix n m α) [Invertible A] : A ⬝ (A⁻¹ ⬝ B) = B :=
   mul_nonsing_inv_cancel_left A B (isUnit_det_of_invertible A)
 #align matrix.mul_inv_cancel_left_of_invertible Matrix.mul_inv_cancel_left_of_invertible
+-/
 
+#print Matrix.inv_mul_cancel_right_of_invertible /-
 @[simp]
 theorem inv_mul_cancel_right_of_invertible (B : Matrix m n α) [Invertible A] : B ⬝ A⁻¹ ⬝ A = B :=
   nonsing_inv_mul_cancel_right A B (isUnit_det_of_invertible A)
 #align matrix.inv_mul_cancel_right_of_invertible Matrix.inv_mul_cancel_right_of_invertible
+-/
 
+#print Matrix.inv_mul_cancel_left_of_invertible /-
 @[simp]
 theorem inv_mul_cancel_left_of_invertible (B : Matrix n m α) [Invertible A] : A⁻¹ ⬝ (A ⬝ B) = B :=
   nonsing_inv_mul_cancel_left A B (isUnit_det_of_invertible A)
 #align matrix.inv_mul_cancel_left_of_invertible Matrix.inv_mul_cancel_left_of_invertible
+-/
 
+#print Matrix.inv_mul_eq_iff_eq_mul_of_invertible /-
 theorem inv_mul_eq_iff_eq_mul_of_invertible (A B C : Matrix n n α) [Invertible A] :
     A⁻¹ ⬝ B = C ↔ B = A ⬝ C :=
   ⟨fun h => by rw [← h, mul_inv_cancel_left_of_invertible], fun h => by
     rw [h, inv_mul_cancel_left_of_invertible]⟩
 #align matrix.inv_mul_eq_iff_eq_mul_of_invertible Matrix.inv_mul_eq_iff_eq_mul_of_invertible
+-/
 
+#print Matrix.mul_inv_eq_iff_eq_mul_of_invertible /-
 theorem mul_inv_eq_iff_eq_mul_of_invertible (A B C : Matrix n n α) [Invertible A] :
     B ⬝ A⁻¹ = C ↔ B = C ⬝ A :=
   ⟨fun h => by rw [← h, inv_mul_cancel_right_of_invertible], fun h => by
     rw [h, mul_inv_cancel_right_of_invertible]⟩
 #align matrix.mul_inv_eq_iff_eq_mul_of_invertible Matrix.mul_inv_eq_iff_eq_mul_of_invertible
+-/
 
+#print Matrix.nonsing_inv_cancel_or_zero /-
 theorem nonsing_inv_cancel_or_zero : A⁻¹ ⬝ A = 1 ∧ A ⬝ A⁻¹ = 1 ∨ A⁻¹ = 0 :=
   by
   by_cases h : IsUnit A.det
   · exact Or.inl ⟨nonsing_inv_mul _ h, mul_nonsing_inv _ h⟩
   · exact Or.inr (nonsing_inv_apply_not_is_unit _ h)
 #align matrix.nonsing_inv_cancel_or_zero Matrix.nonsing_inv_cancel_or_zero
+-/
 
+#print Matrix.det_nonsing_inv_mul_det /-
 theorem det_nonsing_inv_mul_det (h : IsUnit A.det) : A⁻¹.det * A.det = 1 := by
   rw [← det_mul, A.nonsing_inv_mul h, det_one]
 #align matrix.det_nonsing_inv_mul_det Matrix.det_nonsing_inv_mul_det
+-/
 
+#print Matrix.det_nonsing_inv /-
 @[simp]
 theorem det_nonsing_inv : A⁻¹.det = Ring.inverse A.det :=
   by
@@ -413,11 +522,15 @@ theorem det_nonsing_inv : A⁻¹.det = Ring.inverse A.det :=
   · rw [det_is_empty, det_is_empty, Ring.inverse_one]
   · rw [Ring.inverse_non_unit _ h, nonsing_inv_apply_not_is_unit _ h, det_zero ‹_›]
 #align matrix.det_nonsing_inv Matrix.det_nonsing_inv
+-/
 
+#print Matrix.isUnit_nonsing_inv_det /-
 theorem isUnit_nonsing_inv_det (h : IsUnit A.det) : IsUnit A⁻¹.det :=
   isUnit_of_mul_eq_one _ _ (A.det_nonsing_inv_mul_det h)
 #align matrix.is_unit_nonsing_inv_det Matrix.isUnit_nonsing_inv_det
+-/
 
+#print Matrix.nonsing_inv_nonsing_inv /-
 @[simp]
 theorem nonsing_inv_nonsing_inv (h : IsUnit A.det) : A⁻¹⁻¹ = A :=
   calc
@@ -426,60 +539,80 @@ theorem nonsing_inv_nonsing_inv (h : IsUnit A.det) : A⁻¹⁻¹ = A :=
     _ = A := by
       rw [Matrix.mul_assoc, A⁻¹.mul_nonsing_inv (A.is_unit_nonsing_inv_det h), Matrix.mul_one]
 #align matrix.nonsing_inv_nonsing_inv Matrix.nonsing_inv_nonsing_inv
+-/
 
+#print Matrix.isUnit_nonsing_inv_det_iff /-
 theorem isUnit_nonsing_inv_det_iff {A : Matrix n n α} : IsUnit A⁻¹.det ↔ IsUnit A.det := by
   rw [Matrix.det_nonsing_inv, isUnit_ring_inverse]
 #align matrix.is_unit_nonsing_inv_det_iff Matrix.isUnit_nonsing_inv_det_iff
+-/
 
+#print Matrix.invertibleOfIsUnitDet /-
 -- `is_unit.invertible` lifts the proposition `is_unit A` to a constructive inverse of `A`.
 /-- A version of `matrix.invertible_of_det_invertible` with the inverse defeq to `A⁻¹` that is
 therefore noncomputable. -/
 noncomputable def invertibleOfIsUnitDet (h : IsUnit A.det) : Invertible A :=
   ⟨A⁻¹, nonsing_inv_mul A h, mul_nonsing_inv A h⟩
 #align matrix.invertible_of_is_unit_det Matrix.invertibleOfIsUnitDet
+-/
 
+#print Matrix.nonsingInvUnit /-
 /-- A version of `matrix.units_of_det_invertible` with the inverse defeq to `A⁻¹` that is therefore
 noncomputable. -/
 noncomputable def nonsingInvUnit (h : IsUnit A.det) : (Matrix n n α)ˣ :=
   @unitOfInvertible _ _ _ (invertibleOfIsUnitDet A h)
 #align matrix.nonsing_inv_unit Matrix.nonsingInvUnit
+-/
 
+#print Matrix.unitOfDetInvertible_eq_nonsingInvUnit /-
 theorem unitOfDetInvertible_eq_nonsingInvUnit [Invertible A.det] :
     unitOfDetInvertible A = nonsingInvUnit A (isUnit_of_invertible _) := by ext; rfl
 #align matrix.unit_of_det_invertible_eq_nonsing_inv_unit Matrix.unitOfDetInvertible_eq_nonsingInvUnit
+-/
 
 variable {A} {B}
 
+#print Matrix.inv_eq_left_inv /-
 /-- If matrix A is left invertible, then its inverse equals its left inverse. -/
 theorem inv_eq_left_inv (h : B ⬝ A = 1) : A⁻¹ = B :=
   letI := invertible_of_left_inverse _ _ h
   inv_of_eq_nonsing_inv A ▸ invOf_eq_left_inv h
 #align matrix.inv_eq_left_inv Matrix.inv_eq_left_inv
+-/
 
+#print Matrix.inv_eq_right_inv /-
 /-- If matrix A is right invertible, then its inverse equals its right inverse. -/
 theorem inv_eq_right_inv (h : A ⬝ B = 1) : A⁻¹ = B :=
   inv_eq_left_inv (mul_eq_one_comm.2 h)
 #align matrix.inv_eq_right_inv Matrix.inv_eq_right_inv
+-/
 
 section InvEqInv
 
 variable {C : Matrix n n α}
 
+#print Matrix.left_inv_eq_left_inv /-
 /-- The left inverse of matrix A is unique when existing. -/
 theorem left_inv_eq_left_inv (h : B ⬝ A = 1) (g : C ⬝ A = 1) : B = C := by
   rw [← inv_eq_left_inv h, ← inv_eq_left_inv g]
 #align matrix.left_inv_eq_left_inv Matrix.left_inv_eq_left_inv
+-/
 
+#print Matrix.right_inv_eq_right_inv /-
 /-- The right inverse of matrix A is unique when existing. -/
 theorem right_inv_eq_right_inv (h : A ⬝ B = 1) (g : A ⬝ C = 1) : B = C := by
   rw [← inv_eq_right_inv h, ← inv_eq_right_inv g]
 #align matrix.right_inv_eq_right_inv Matrix.right_inv_eq_right_inv
+-/
 
+#print Matrix.right_inv_eq_left_inv /-
 /-- The right inverse of matrix A equals the left inverse of A when they exist. -/
 theorem right_inv_eq_left_inv (h : A ⬝ B = 1) (g : C ⬝ A = 1) : B = C := by
   rw [← inv_eq_right_inv h, ← inv_eq_left_inv g]
 #align matrix.right_inv_eq_left_inv Matrix.right_inv_eq_left_inv
+-/
 
+#print Matrix.inv_inj /-
 theorem inv_inj (h : A⁻¹ = B⁻¹) (h' : IsUnit A.det) : A = B :=
   by
   refine' left_inv_eq_left_inv (mul_nonsing_inv _ h') _
@@ -487,11 +620,13 @@ theorem inv_inj (h : A⁻¹ = B⁻¹) (h' : IsUnit A.det) : A = B :=
   refine' mul_nonsing_inv _ _
   rwa [← is_unit_nonsing_inv_det_iff, ← h, is_unit_nonsing_inv_det_iff]
 #align matrix.inv_inj Matrix.inv_inj
+-/
 
 end InvEqInv
 
 variable (A)
 
+#print Matrix.inv_zero /-
 @[simp]
 theorem inv_zero : (0 : Matrix n n α)⁻¹ = 0 :=
   by
@@ -506,32 +641,42 @@ theorem inv_zero : (0 : Matrix n n α)⁻¹ = 0 :=
     refine' nonsing_inv_apply_not_is_unit _ _
     simp [hn]
 #align matrix.inv_zero Matrix.inv_zero
+-/
 
 noncomputable instance : InvOneClass (Matrix n n α) :=
   { Matrix.hasOne, Matrix.hasInv with inv_one := inv_eq_left_inv (by simp) }
 
+#print Matrix.inv_smul /-
 theorem inv_smul (k : α) [Invertible k] (h : IsUnit A.det) : (k • A)⁻¹ = ⅟ k • A⁻¹ :=
   inv_eq_left_inv (by simp [h, smul_smul])
 #align matrix.inv_smul Matrix.inv_smul
+-/
 
+#print Matrix.inv_smul' /-
 theorem inv_smul' (k : αˣ) (h : IsUnit A.det) : (k • A)⁻¹ = k⁻¹ • A⁻¹ :=
   inv_eq_left_inv (by simp [h, smul_smul])
 #align matrix.inv_smul' Matrix.inv_smul'
+-/
 
+#print Matrix.inv_adjugate /-
 theorem inv_adjugate (A : Matrix n n α) (h : IsUnit A.det) : (adjugate A)⁻¹ = h.Unit⁻¹ • A :=
   by
   refine' inv_eq_left_inv _
   rw [smul_mul, mul_adjugate, Units.smul_def, smul_smul, h.coe_inv_mul, one_smul]
 #align matrix.inv_adjugate Matrix.inv_adjugate
+-/
 
 section Diagonal
 
+#print Matrix.diagonalInvertible /-
 /-- `diagonal v` is invertible if `v` is -/
 def diagonalInvertible {α} [NonAssocSemiring α] (v : n → α) [Invertible v] :
     Invertible (diagonal v) :=
   Invertible.map (diagonalRingHom n α) v
 #align matrix.diagonal_invertible Matrix.diagonalInvertible
+-/
 
+#print Matrix.invOf_diagonal_eq /-
 theorem invOf_diagonal_eq {α} [Semiring α] (v : n → α) [Invertible v] [Invertible (diagonal v)] :
     ⅟ (diagonal v) = diagonal (⅟ v) :=
   by
@@ -539,7 +684,9 @@ theorem invOf_diagonal_eq {α} [Semiring α] (v : n → α) [Invertible v] [Inve
   haveI := Invertible.subsingleton (diagonal v)
   convert (rfl : ⅟ (diagonal v) = _)
 #align matrix.inv_of_diagonal_eq Matrix.invOf_diagonal_eq
+-/
 
+#print Matrix.invertibleOfDiagonalInvertible /-
 /-- `v` is invertible if `diagonal v` is -/
 def invertibleOfDiagonalInvertible (v : n → α) [Invertible (diagonal v)] : Invertible v
     where
@@ -561,7 +708,9 @@ def invertibleOfDiagonalInvertible (v : n → α) [Invertible (diagonal v)] : In
       rw [mul_left_comm, mul_prod_erase _ _ (Finset.mem_univ _), ← det_diagonal]
       exact mul_invOf_self _
 #align matrix.invertible_of_diagonal_invertible Matrix.invertibleOfDiagonalInvertible
+-/
 
+#print Matrix.diagonalInvertibleEquivInvertible /-
 /-- Together `matrix.diagonal_invertible` and `matrix.invertible_of_diagonal_invertible` form an
 equivalence, although both sides of the equiv are subsingleton anyway. -/
 @[simps]
@@ -572,14 +721,18 @@ def diagonalInvertibleEquivInvertible (v : n → α) : Invertible (diagonal v) 
   left_inv _ := Subsingleton.elim _ _
   right_inv _ := Subsingleton.elim _ _
 #align matrix.diagonal_invertible_equiv_invertible Matrix.diagonalInvertibleEquivInvertible
+-/
 
+#print Matrix.isUnit_diagonal /-
 /-- When lowered to a prop, `matrix.diagonal_invertible_equiv_invertible` forms an `iff`. -/
 @[simp]
 theorem isUnit_diagonal {v : n → α} : IsUnit (diagonal v) ↔ IsUnit v := by
   simp only [← nonempty_invertible_iff_isUnit,
     (diagonal_invertible_equiv_invertible v).nonempty_congr]
 #align matrix.is_unit_diagonal Matrix.isUnit_diagonal
+-/
 
+#print Matrix.inv_diagonal /-
 theorem inv_diagonal (v : n → α) : (diagonal v)⁻¹ = diagonal (Ring.inverse v) :=
   by
   rw [nonsing_inv_eq_ring_inverse]
@@ -591,9 +744,11 @@ theorem inv_diagonal (v : n → α) : (diagonal v)⁻¹ = diagonal (Ring.inverse
   · have := is_unit_diagonal.not.mpr h
     rw [Ring.inverse_non_unit _ h, Pi.zero_def, diagonal_zero, Ring.inverse_non_unit _ this]
 #align matrix.inv_diagonal Matrix.inv_diagonal
+-/
 
 end Diagonal
 
+#print Matrix.inv_inv_inv /-
 @[simp]
 theorem inv_inv_inv (A : Matrix n n α) : A⁻¹⁻¹⁻¹ = A⁻¹ :=
   by
@@ -601,15 +756,19 @@ theorem inv_inv_inv (A : Matrix n n α) : A⁻¹⁻¹⁻¹ = A⁻¹ :=
   · rw [nonsing_inv_nonsing_inv _ h]
   · simp [nonsing_inv_apply_not_is_unit _ h]
 #align matrix.inv_inv_inv Matrix.inv_inv_inv
+-/
 
+#print Matrix.mul_inv_rev /-
 theorem mul_inv_rev (A B : Matrix n n α) : (A ⬝ B)⁻¹ = B⁻¹ ⬝ A⁻¹ :=
   by
   simp only [inv_def]
   rw [Matrix.smul_mul, Matrix.mul_smul, smul_smul, det_mul, adjugate_mul_distrib,
     Ring.mul_inverse_rev]
 #align matrix.mul_inv_rev Matrix.mul_inv_rev
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print Matrix.list_prod_inv_reverse /-
 /-- A version of `list.prod_inv_reverse` for `matrix.has_inv`. -/
 theorem list_prod_inv_reverse : ∀ l : List (Matrix n n α), l.Prod⁻¹ = (l.reverse.map Inv.inv).Prod
   | [] => by rw [List.reverse_nil, List.map_nil, List.prod_nil, inv_one]
@@ -617,7 +776,9 @@ theorem list_prod_inv_reverse : ∀ l : List (Matrix n n α), l.Prod⁻¹ = (l.r
     rw [List.reverse_cons', List.map_concat, List.prod_concat, List.prod_cons, Matrix.mul_eq_mul,
       Matrix.mul_eq_mul, mul_inv_rev, list_prod_inv_reverse]
 #align matrix.list_prod_inv_reverse Matrix.list_prod_inv_reverse
+-/
 
+#print Matrix.det_smul_inv_mulVec_eq_cramer /-
 /-- One form of **Cramer's rule**. See `matrix.mul_vec_cramer` for a stronger form. -/
 @[simp]
 theorem det_smul_inv_mulVec_eq_cramer (A : Matrix n n α) (b : n → α) (h : IsUnit A.det) :
@@ -625,7 +786,9 @@ theorem det_smul_inv_mulVec_eq_cramer (A : Matrix n n α) (b : n → α) (h : Is
   rw [cramer_eq_adjugate_mul_vec, A.nonsing_inv_apply h, ← smul_mul_vec_assoc, smul_smul,
     h.mul_coe_inv, one_smul]
 #align matrix.det_smul_inv_mul_vec_eq_cramer Matrix.det_smul_inv_mulVec_eq_cramer
+-/
 
+#print Matrix.det_smul_inv_vecMul_eq_cramer_transpose /-
 /-- One form of **Cramer's rule**. See `matrix.mul_vec_cramer` for a stronger form. -/
 @[simp]
 theorem det_smul_inv_vecMul_eq_cramer_transpose (A : Matrix n n α) (b : n → α) (h : IsUnit A.det) :
@@ -633,6 +796,7 @@ theorem det_smul_inv_vecMul_eq_cramer_transpose (A : Matrix n n α) (b : n → 
   rw [← A⁻¹.transpose_transpose, vec_mul_transpose, transpose_nonsing_inv, ← det_transpose,
     Aᵀ.det_smul_inv_mulVec_eq_cramer _ (is_unit_det_transpose A h)]
 #align matrix.det_smul_inv_vec_mul_eq_cramer_transpose Matrix.det_smul_inv_vecMul_eq_cramer_transpose
+-/
 
 /-! ### Inverses of permutated matrices
 
@@ -647,13 +811,16 @@ variable [Fintype m]
 
 variable [DecidableEq m]
 
+#print Matrix.submatrixEquivInvertible /-
 /-- `A.submatrix e₁ e₂` is invertible if `A` is -/
 def submatrixEquivInvertible (A : Matrix m m α) (e₁ e₂ : n ≃ m) [Invertible A] :
     Invertible (A.submatrix e₁ e₂) :=
   invertibleOfRightInverse _ ((⅟ A).submatrix e₂ e₁) <| by
     rw [Matrix.submatrix_mul_equiv, Matrix.mul_invOf_self, submatrix_one_equiv]
 #align matrix.submatrix_equiv_invertible Matrix.submatrixEquivInvertible
+-/
 
+#print Matrix.invertibleOfSubmatrixEquivInvertible /-
 /-- `A` is invertible if `A.submatrix e₁ e₂` is -/
 def invertibleOfSubmatrixEquivInvertible (A : Matrix m m α) (e₁ e₂ : n ≃ m)
     [Invertible (A.submatrix e₁ e₂)] : Invertible A :=
@@ -665,7 +832,9 @@ def invertibleOfSubmatrixEquivInvertible (A : Matrix m m α) (e₁ e₂ : n ≃
       rw [this]
     rw [Matrix.submatrix_mul_equiv, Matrix.mul_invOf_self, submatrix_one_equiv]
 #align matrix.invertible_of_submatrix_equiv_invertible Matrix.invertibleOfSubmatrixEquivInvertible
+-/
 
+#print Matrix.invOf_submatrix_equiv_eq /-
 theorem invOf_submatrix_equiv_eq (A : Matrix m m α) (e₁ e₂ : n ≃ m) [Invertible A]
     [Invertible (A.submatrix e₁ e₂)] : ⅟ (A.submatrix e₁ e₂) = (⅟ A).submatrix e₂ e₁ :=
   by
@@ -673,7 +842,9 @@ theorem invOf_submatrix_equiv_eq (A : Matrix m m α) (e₁ e₂ : n ≃ m) [Inve
   haveI := Invertible.subsingleton (A.submatrix e₁ e₂)
   convert (rfl : ⅟ (A.submatrix e₁ e₂) = _)
 #align matrix.inv_of_submatrix_equiv_eq Matrix.invOf_submatrix_equiv_eq
+-/
 
+#print Matrix.submatrixEquivInvertibleEquivInvertible /-
 /-- Together `matrix.submatrix_equiv_invertible` and
 `matrix.invertible_of_submatrix_equiv_invertible` form an equivalence, although both sides of the
 equiv are subsingleton anyway. -/
@@ -686,6 +857,7 @@ def submatrixEquivInvertibleEquivInvertible (A : Matrix m m α) (e₁ e₂ : n 
   left_inv _ := Subsingleton.elim _ _
   right_inv _ := Subsingleton.elim _ _
 #align matrix.submatrix_equiv_invertible_equiv_invertible Matrix.submatrixEquivInvertibleEquivInvertible
+-/
 
 #print Matrix.isUnit_submatrix_equiv /-
 /-- When lowered to a prop, `matrix.invertible_of_submatrix_equiv_invertible` forms an `iff`. -/
@@ -697,6 +869,7 @@ theorem isUnit_submatrix_equiv {A : Matrix m m α} (e₁ e₂ : n ≃ m) :
 #align matrix.is_unit_submatrix_equiv Matrix.isUnit_submatrix_equiv
 -/
 
+#print Matrix.inv_submatrix_equiv /-
 @[simp]
 theorem inv_submatrix_equiv (A : Matrix m m α) (e₁ e₂ : n ≃ m) :
     (A.submatrix e₁ e₂)⁻¹ = A⁻¹.submatrix e₂ e₁ :=
@@ -709,10 +882,13 @@ theorem inv_submatrix_equiv (A : Matrix m m α) (e₁ e₂ : n ≃ m) :
     simp_rw [nonsing_inv_eq_ring_inverse, Ring.inverse_non_unit _ h, Ring.inverse_non_unit _ this,
       submatrix_zero, Pi.zero_apply]
 #align matrix.inv_submatrix_equiv Matrix.inv_submatrix_equiv
+-/
 
+#print Matrix.inv_reindex /-
 theorem inv_reindex (e₁ e₂ : n ≃ m) (A : Matrix n n α) : (reindex e₁ e₂ A)⁻¹ = reindex e₂ e₁ A⁻¹ :=
   inv_submatrix_equiv A e₁.symm e₂.symm
 #align matrix.inv_reindex Matrix.inv_reindex
+-/
 
 end Submatrix
 
@@ -723,15 +899,19 @@ section Det
 
 variable [Fintype m] [DecidableEq m]
 
+#print Matrix.det_conj /-
 /-- A variant of `matrix.det_units_conj`. -/
 theorem det_conj {M : Matrix m m α} (h : IsUnit M) (N : Matrix m m α) : det (M ⬝ N ⬝ M⁻¹) = det N :=
   by rw [← h.unit_spec, ← coe_units_inv, det_units_conj]
 #align matrix.det_conj Matrix.det_conj
+-/
 
+#print Matrix.det_conj' /-
 /-- A variant of `matrix.det_units_conj'`. -/
 theorem det_conj' {M : Matrix m m α} (h : IsUnit M) (N : Matrix m m α) :
     det (M⁻¹ ⬝ N ⬝ M) = det N := by rw [← h.unit_spec, ← coe_units_inv, det_units_conj']
 #align matrix.det_conj' Matrix.det_conj'
+-/
 
 end Det
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

@@ -166,7 +166,6 @@ theorem mul_eq_one_comm : A ⬝ B = 1 ↔ B ⬝ A = 1 :=
     _ = B ⬝ (A ⬝ B ⬝ ⅟ B) := by simp only [Matrix.mul_assoc]
     _ = B ⬝ ⅟ B := by rw [h, Matrix.one_mul]
     _ = 1 := Matrix.mul_invOf_self B
-    
 #align matrix.mul_eq_one_comm Matrix.mul_eq_one_comm
 
 variable (A B)
@@ -426,7 +425,6 @@ theorem nonsing_inv_nonsing_inv (h : IsUnit A.det) : A⁻¹⁻¹ = A :=
     _ = A ⬝ A⁻¹ ⬝ A⁻¹⁻¹ := by rw [A.mul_nonsing_inv h]
     _ = A := by
       rw [Matrix.mul_assoc, A⁻¹.mul_nonsing_inv (A.is_unit_nonsing_inv_det h), Matrix.mul_one]
-    
 #align matrix.nonsing_inv_nonsing_inv Matrix.nonsing_inv_nonsing_inv
 
 theorem isUnit_nonsing_inv_det_iff {A : Matrix n n α} : IsUnit A⁻¹.det ↔ IsUnit A.det := by

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

@@ -115,7 +115,7 @@ def invertibleOfDetInvertible [Invertible A.det] : Invertible A
 #align matrix.invertible_of_det_invertible Matrix.invertibleOfDetInvertible
 
 theorem invOf_eq [Invertible A.det] [Invertible A] : ⅟ A = ⅟ A.det • A.adjugate := by
-  letI := invertible_of_det_invertible A; convert(rfl : ⅟ A = _)
+  letI := invertible_of_det_invertible A; convert (rfl : ⅟ A = _)
 #align matrix.inv_of_eq Matrix.invOf_eq
 
 /-- `A.det` is invertible if `A` has a left inverse. -/
@@ -140,7 +140,7 @@ def detInvertibleOfInvertible [Invertible A] : Invertible A.det :=
 #align matrix.det_invertible_of_invertible Matrix.detInvertibleOfInvertible
 
 theorem det_invOf [Invertible A] [Invertible A.det] : (⅟ A).det = ⅟ A.det := by
-  letI := det_invertible_of_invertible A; convert(rfl : _ = ⅟ A.det)
+  letI := det_invertible_of_invertible A; convert (rfl : _ = ⅟ A.det)
 #align matrix.det_inv_of Matrix.det_invOf
 
 /-- Together `matrix.det_invertible_of_invertible` and `matrix.invertible_of_det_invertible` form an
@@ -539,7 +539,7 @@ theorem invOf_diagonal_eq {α} [Semiring α] (v : n → α) [Invertible v] [Inve
   by
   letI := diagonal_invertible v
   haveI := Invertible.subsingleton (diagonal v)
-  convert(rfl : ⅟ (diagonal v) = _)
+  convert (rfl : ⅟ (diagonal v) = _)
 #align matrix.inv_of_diagonal_eq Matrix.invOf_diagonal_eq
 
 /-- `v` is invertible if `diagonal v` is -/
@@ -673,7 +673,7 @@ theorem invOf_submatrix_equiv_eq (A : Matrix m m α) (e₁ e₂ : n ≃ m) [Inve
   by
   letI := submatrix_equiv_invertible A e₁ e₂
   haveI := Invertible.subsingleton (A.submatrix e₁ e₂)
-  convert(rfl : ⅟ (A.submatrix e₁ e₂) = _)
+  convert (rfl : ⅟ (A.submatrix e₁ e₂) = _)
 #align matrix.inv_of_submatrix_equiv_eq Matrix.invOf_submatrix_equiv_eq
 
 /-- Together `matrix.submatrix_equiv_invertible` and

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

@@ -500,7 +500,7 @@ theorem inv_zero : (0 : Matrix n n α)⁻¹ = 0 :=
   cases' subsingleton_or_nontrivial α with ht ht
   · simp
   cases' (Fintype.card n).zero_le.eq_or_lt with hc hc
-  · rw [eq_comm, Fintype.card_eq_zero_iff] at hc
+  · rw [eq_comm, Fintype.card_eq_zero_iff] at hc 
     haveI := hc
     ext i
     exact (IsEmpty.false i).elim

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -61,7 +61,7 @@ universe u u' v
 
 variable {l : Type _} {m : Type u} {n : Type u'} {α : Type v}
 
-open Matrix BigOperators
+open scoped Matrix BigOperators
 
 open Equiv Equiv.Perm Finset
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -72,67 +72,31 @@ section Invertible
 
 variable [Fintype n] [DecidableEq n] [CommRing α]
 
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-Case conversion may be inaccurate. Consider using '#align matrix.inv_of_mul_self Matrix.invOf_mul_selfₓ'. -/
 /-- A copy of `inv_of_mul_self` using `⬝` not `*`. -/
 protected theorem invOf_mul_self (A : Matrix n n α) [Invertible A] : ⅟ A ⬝ A = 1 :=
   invOf_mul_self A
 #align matrix.inv_of_mul_self Matrix.invOf_mul_self
 
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 /-- A copy of `mul_inv_of_self` using `⬝` not `*`. -/
 protected theorem mul_invOf_self (A : Matrix n n α) [Invertible A] : A ⬝ ⅟ A = 1 :=
   mul_invOf_self A
 #align matrix.mul_inv_of_self Matrix.mul_invOf_self
 
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 /-- A copy of `inv_of_mul_self_assoc` using `⬝` not `*`. -/
 protected theorem invOf_mul_self_assoc (A : Matrix n n α) (B : Matrix n m α) [Invertible A] :
     ⅟ A ⬝ (A ⬝ B) = B := by rw [← Matrix.mul_assoc, Matrix.invOf_mul_self, Matrix.one_mul]
 #align matrix.inv_of_mul_self_assoc Matrix.invOf_mul_self_assoc
 
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 /-- A copy of `mul_inv_of_self_assoc` using `⬝` not `*`. -/
 protected theorem mul_invOf_self_assoc (A : Matrix n n α) (B : Matrix n m α) [Invertible A] :
     A ⬝ (⅟ A ⬝ B) = B := by rw [← Matrix.mul_assoc, Matrix.mul_invOf_self, Matrix.one_mul]
 #align matrix.mul_inv_of_self_assoc Matrix.mul_invOf_self_assoc
 
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 /-- A copy of `mul_inv_of_mul_self_cancel` using `⬝` not `*`. -/
 protected theorem mul_invOf_mul_self_cancel (A : Matrix m n α) (B : Matrix n n α) [Invertible B] :
     A ⬝ ⅟ B ⬝ B = A := by rw [Matrix.mul_assoc, Matrix.invOf_mul_self, Matrix.mul_one]
 #align matrix.mul_inv_of_mul_self_cancel Matrix.mul_invOf_mul_self_cancel
 
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 /-- A copy of `mul_mul_inv_of_self_cancel` using `⬝` not `*`. -/
 protected theorem mul_mul_invOf_self_cancel (A : Matrix m n α) (B : Matrix n n α) [Invertible B] :
     A ⬝ B ⬝ ⅟ B = A := by rw [Matrix.mul_assoc, Matrix.mul_invOf_self, Matrix.mul_one]
@@ -140,12 +104,6 @@ protected theorem mul_mul_invOf_self_cancel (A : Matrix m n α) (B : Matrix n n
 
 variable (A : Matrix n n α) (B : Matrix n n α)
 
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 /-- If `A.det` has a constructive inverse, produce one for `A`. -/
 def invertibleOfDetInvertible [Invertible A.det] : Invertible A
     where
@@ -156,22 +114,10 @@ def invertibleOfDetInvertible [Invertible A.det] : Invertible A
     rw [smul_mul_assoc, Matrix.mul_eq_mul, adjugate_mul, smul_smul, invOf_mul_self, one_smul]
 #align matrix.invertible_of_det_invertible Matrix.invertibleOfDetInvertible
 
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 theorem invOf_eq [Invertible A.det] [Invertible A] : ⅟ A = ⅟ A.det • A.adjugate := by
   letI := invertible_of_det_invertible A; convert(rfl : ⅟ A = _)
 #align matrix.inv_of_eq Matrix.invOf_eq
 
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 /-- `A.det` is invertible if `A` has a left inverse. -/
 def detInvertibleOfLeftInverse (h : B ⬝ A = 1) : Invertible A.det
     where
@@ -180,12 +126,6 @@ def detInvertibleOfLeftInverse (h : B ⬝ A = 1) : Invertible A.det
   invOf_mul_self := by rw [← det_mul, h, det_one]
 #align matrix.det_invertible_of_left_inverse Matrix.detInvertibleOfLeftInverse
 
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 /-- `A.det` is invertible if `A` has a right inverse. -/
 def detInvertibleOfRightInverse (h : A ⬝ B = 1) : Invertible A.det
     where
@@ -194,33 +134,15 @@ def detInvertibleOfRightInverse (h : A ⬝ B = 1) : Invertible A.det
   invOf_mul_self := by rw [mul_comm, ← det_mul, h, det_one]
 #align matrix.det_invertible_of_right_inverse Matrix.detInvertibleOfRightInverse
 
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 /-- If `A` has a constructive inverse, produce one for `A.det`. -/
 def detInvertibleOfInvertible [Invertible A] : Invertible A.det :=
   detInvertibleOfLeftInverse A (⅟ A) (invOf_mul_self _)
 #align matrix.det_invertible_of_invertible Matrix.detInvertibleOfInvertible
 
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 theorem det_invOf [Invertible A] [Invertible A.det] : (⅟ A).det = ⅟ A.det := by
   letI := det_invertible_of_invertible A; convert(rfl : _ = ⅟ A.det)
 #align matrix.det_inv_of Matrix.det_invOf
 
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 /-- Together `matrix.det_invertible_of_invertible` and `matrix.invertible_of_det_invertible` form an
 equivalence, although both sides of the equiv are subsingleton anyway. -/
 @[simps]
@@ -234,12 +156,6 @@ def invertibleEquivDetInvertible : Invertible A ≃ Invertible A.det
 
 variable {A B}
 
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 theorem mul_eq_one_comm : A ⬝ B = 1 ↔ B ⬝ A = 1 :=
   suffices ∀ A B, A ⬝ B = 1 → B ⬝ A = 1 from ⟨this A B, this B A⟩
   fun A B h => by
@@ -255,46 +171,22 @@ theorem mul_eq_one_comm : A ⬝ B = 1 ↔ B ⬝ A = 1 :=
 
 variable (A B)
 
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 /-- We can construct an instance of invertible A if A has a left inverse. -/
 def invertibleOfLeftInverse (h : B ⬝ A = 1) : Invertible A :=
   ⟨B, h, mul_eq_one_comm.mp h⟩
 #align matrix.invertible_of_left_inverse Matrix.invertibleOfLeftInverse
 
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 /-- We can construct an instance of invertible A if A has a right inverse. -/
 def invertibleOfRightInverse (h : A ⬝ B = 1) : Invertible A :=
   ⟨B, mul_eq_one_comm.mp h, h⟩
 #align matrix.invertible_of_right_inverse Matrix.invertibleOfRightInverse
 
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 /-- The transpose of an invertible matrix is invertible. -/
 instance invertibleTranspose [Invertible A] : Invertible Aᵀ :=
   haveI : Invertible Aᵀ.det := by simpa using det_invertible_of_invertible A
   invertible_of_det_invertible Aᵀ
 #align matrix.invertible_transpose Matrix.invertibleTranspose
 
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 /-- A matrix is invertible if the transpose is invertible. -/
 def invertibleOfInvertibleTranspose [Invertible Aᵀ] : Invertible A :=
   by
@@ -302,12 +194,6 @@ def invertibleOfInvertibleTranspose [Invertible Aᵀ] : Invertible A :=
   infer_instance
 #align matrix.invertible__of_invertible_transpose Matrix.invertibleOfInvertibleTranspose
 
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 /-- A matrix is invertible if the conjugate transpose is invertible. -/
 def invertibleOfInvertibleConjTranspose [StarRing α] [Invertible Aᴴ] : Invertible A :=
   by
@@ -315,23 +201,11 @@ def invertibleOfInvertibleConjTranspose [StarRing α] [Invertible Aᴴ] : Invert
   infer_instance
 #align matrix.invertible_of_invertible_conj_transpose Matrix.invertibleOfInvertibleConjTranspose
 
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 /-- Given a proof that `A.det` has a constructive inverse, lift `A` to `(matrix n n α)ˣ`-/
 def unitOfDetInvertible [Invertible A.det] : (Matrix n n α)ˣ :=
   @unitOfInvertible _ _ A (invertibleOfDetInvertible A)
 #align matrix.unit_of_det_invertible Matrix.unitOfDetInvertible
 
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 /-- When lowered to a prop, `matrix.invertible_equiv_det_invertible` forms an `iff`. -/
 theorem isUnit_iff_isUnit_det : IsUnit A ↔ IsUnit A.det := by
   simp only [← nonempty_invertible_iff_isUnit, (invertible_equiv_det_invertible A).nonempty_congr]
@@ -340,74 +214,32 @@ theorem isUnit_iff_isUnit_det : IsUnit A ↔ IsUnit A.det := by
 /-! #### Variants of the statements above with `is_unit`-/
 
 
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 theorem isUnit_det_of_invertible [Invertible A] : IsUnit A.det :=
   @isUnit_of_invertible _ _ _ (detInvertibleOfInvertible A)
 #align matrix.is_unit_det_of_invertible Matrix.isUnit_det_of_invertible
 
 variable {A B}
 
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 theorem isUnit_of_left_inverse (h : B ⬝ A = 1) : IsUnit A :=
   ⟨⟨A, B, mul_eq_one_comm.mp h, h⟩, rfl⟩
 #align matrix.is_unit_of_left_inverse Matrix.isUnit_of_left_inverse
 
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 theorem isUnit_of_right_inverse (h : A ⬝ B = 1) : IsUnit A :=
   ⟨⟨A, B, h, mul_eq_one_comm.mp h⟩, rfl⟩
 #align matrix.is_unit_of_right_inverse Matrix.isUnit_of_right_inverse
 
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 theorem isUnit_det_of_left_inverse (h : B ⬝ A = 1) : IsUnit A.det :=
   @isUnit_of_invertible _ _ _ (detInvertibleOfLeftInverse _ _ h)
 #align matrix.is_unit_det_of_left_inverse Matrix.isUnit_det_of_left_inverse
 
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 theorem isUnit_det_of_right_inverse (h : A ⬝ B = 1) : IsUnit A.det :=
   @isUnit_of_invertible _ _ _ (detInvertibleOfRightInverse _ _ h)
 #align matrix.is_unit_det_of_right_inverse Matrix.isUnit_det_of_right_inverse
 
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 theorem det_ne_zero_of_left_inverse [Nontrivial α] (h : B ⬝ A = 1) : A.det ≠ 0 :=
   (isUnit_det_of_left_inverse h).NeZero
 #align matrix.det_ne_zero_of_left_inverse Matrix.det_ne_zero_of_left_inverse
 
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 theorem det_ne_zero_of_right_inverse [Nontrivial α] (h : A ⬝ B = 1) : A.det ≠ 0 :=
   (isUnit_det_of_right_inverse h).NeZero
 #align matrix.det_ne_zero_of_right_inverse Matrix.det_ne_zero_of_right_inverse
@@ -418,12 +250,6 @@ variable [Fintype n] [DecidableEq n] [CommRing α]
 
 variable (A : Matrix n n α) (B : Matrix n n α)
 
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 theorem isUnit_det_transpose (h : IsUnit A.det) : IsUnit Aᵀ.det := by rw [det_transpose]; exact h
 #align matrix.is_unit_det_transpose Matrix.isUnit_det_transpose
 
@@ -434,42 +260,18 @@ theorem isUnit_det_transpose (h : IsUnit A.det) : IsUnit Aᵀ.det := by rw [det_
 noncomputable instance : Inv (Matrix n n α) :=
   ⟨fun A => Ring.inverse A.det • A.adjugate⟩
 
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 theorem inv_def (A : Matrix n n α) : A⁻¹ = Ring.inverse A.det • A.adjugate :=
   rfl
 #align matrix.inv_def Matrix.inv_def
 
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 theorem nonsing_inv_apply_not_isUnit (h : ¬IsUnit A.det) : A⁻¹ = 0 := by
   rw [inv_def, Ring.inverse_non_unit _ h, zero_smul]
 #align matrix.nonsing_inv_apply_not_is_unit Matrix.nonsing_inv_apply_not_isUnit
 
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 theorem nonsing_inv_apply (h : IsUnit A.det) : A⁻¹ = (↑h.Unit⁻¹ : α) • A.adjugate := by
   rw [inv_def, ← Ring.inverse_unit h.unit, IsUnit.unit_spec]
 #align matrix.nonsing_inv_apply Matrix.nonsing_inv_apply
 
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 /-- The nonsingular inverse is the same as `inv_of` when `A` is invertible. -/
 @[simp]
 theorem invOf_eq_nonsing_inv [Invertible A] : ⅟ A = A⁻¹ :=
@@ -478,12 +280,6 @@ theorem invOf_eq_nonsing_inv [Invertible A] : ⅟ A = A⁻¹ :=
   rw [inv_def, Ring.inverse_invertible, inv_of_eq]
 #align matrix.inv_of_eq_nonsing_inv Matrix.invOf_eq_nonsing_inv
 
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 /-- Coercing the result of `units.has_inv` is the same as coercing first and applying the
 nonsingular inverse. -/
 @[simp, norm_cast]
@@ -493,12 +289,6 @@ theorem coe_units_inv (A : (Matrix n n α)ˣ) : ↑A⁻¹ = (A⁻¹ : Matrix n n
   rw [← inv_of_eq_nonsing_inv, invOf_units]
 #align matrix.coe_units_inv Matrix.coe_units_inv
 
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 /-- The nonsingular inverse is the same as the general `ring.inverse`. -/
 theorem nonsing_inv_eq_ring_inverse : A⁻¹ = Ring.inverse A :=
   by
@@ -509,33 +299,15 @@ theorem nonsing_inv_eq_ring_inverse : A⁻¹ = Ring.inverse A :=
     rw [Ring.inverse_non_unit _ h, nonsing_inv_apply_not_is_unit A h_det]
 #align matrix.nonsing_inv_eq_ring_inverse Matrix.nonsing_inv_eq_ring_inverse
 
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 theorem transpose_nonsing_inv : A⁻¹ᵀ = Aᵀ⁻¹ := by
   rw [inv_def, inv_def, transpose_smul, det_transpose, adjugate_transpose]
 #align matrix.transpose_nonsing_inv Matrix.transpose_nonsing_inv
 
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 theorem conjTranspose_nonsing_inv [StarRing α] : A⁻¹ᴴ = Aᴴ⁻¹ := by
   rw [inv_def, inv_def, conj_transpose_smul, det_conj_transpose, adjugate_conj_transpose,
     Ring.inverse_star]
 #align matrix.conj_transpose_nonsing_inv Matrix.conjTranspose_nonsing_inv
 
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 /-- The `nonsing_inv` of `A` is a right inverse. -/
 @[simp]
 theorem mul_nonsing_inv (h : IsUnit A.det) : A ⬝ A⁻¹ = 1 :=
@@ -544,12 +316,6 @@ theorem mul_nonsing_inv (h : IsUnit A.det) : A ⬝ A⁻¹ = 1 :=
   rw [← inv_of_eq_nonsing_inv, Matrix.mul_invOf_self]
 #align matrix.mul_nonsing_inv Matrix.mul_nonsing_inv
 
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 /-- The `nonsing_inv` of `A` is a left inverse. -/
 @[simp]
 theorem nonsing_inv_mul (h : IsUnit A.det) : A⁻¹ ⬝ A = 1 :=
@@ -560,157 +326,73 @@ theorem nonsing_inv_mul (h : IsUnit A.det) : A⁻¹ ⬝ A = 1 :=
 
 instance [Invertible A] : Invertible A⁻¹ := by rw [← inv_of_eq_nonsing_inv]; infer_instance
 
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 @[simp]
 theorem inv_inv_of_invertible [Invertible A] : A⁻¹⁻¹ = A := by
   simp only [← inv_of_eq_nonsing_inv, invOf_invOf]
 #align matrix.inv_inv_of_invertible Matrix.inv_inv_of_invertible
 
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 @[simp]
 theorem mul_nonsing_inv_cancel_right (B : Matrix m n α) (h : IsUnit A.det) : B ⬝ A ⬝ A⁻¹ = B := by
   simp [Matrix.mul_assoc, mul_nonsing_inv A h]
 #align matrix.mul_nonsing_inv_cancel_right Matrix.mul_nonsing_inv_cancel_right
 
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 @[simp]
 theorem mul_nonsing_inv_cancel_left (B : Matrix n m α) (h : IsUnit A.det) : A ⬝ (A⁻¹ ⬝ B) = B := by
   simp [← Matrix.mul_assoc, mul_nonsing_inv A h]
 #align matrix.mul_nonsing_inv_cancel_left Matrix.mul_nonsing_inv_cancel_left
 
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 @[simp]
 theorem nonsing_inv_mul_cancel_right (B : Matrix m n α) (h : IsUnit A.det) : B ⬝ A⁻¹ ⬝ A = B := by
   simp [Matrix.mul_assoc, nonsing_inv_mul A h]
 #align matrix.nonsing_inv_mul_cancel_right Matrix.nonsing_inv_mul_cancel_right
 
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 @[simp]
 theorem nonsing_inv_mul_cancel_left (B : Matrix n m α) (h : IsUnit A.det) : A⁻¹ ⬝ (A ⬝ B) = B := by
   simp [← Matrix.mul_assoc, nonsing_inv_mul A h]
 #align matrix.nonsing_inv_mul_cancel_left Matrix.nonsing_inv_mul_cancel_left
 
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 @[simp]
 theorem mul_inv_of_invertible [Invertible A] : A ⬝ A⁻¹ = 1 :=
   mul_nonsing_inv A (isUnit_det_of_invertible A)
 #align matrix.mul_inv_of_invertible Matrix.mul_inv_of_invertible
 
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 @[simp]
 theorem inv_mul_of_invertible [Invertible A] : A⁻¹ ⬝ A = 1 :=
   nonsing_inv_mul A (isUnit_det_of_invertible A)
 #align matrix.inv_mul_of_invertible Matrix.inv_mul_of_invertible
 
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 @[simp]
 theorem mul_inv_cancel_right_of_invertible (B : Matrix m n α) [Invertible A] : B ⬝ A ⬝ A⁻¹ = B :=
   mul_nonsing_inv_cancel_right A B (isUnit_det_of_invertible A)
 #align matrix.mul_inv_cancel_right_of_invertible Matrix.mul_inv_cancel_right_of_invertible
 
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 @[simp]
 theorem mul_inv_cancel_left_of_invertible (B : Matrix n m α) [Invertible A] : A ⬝ (A⁻¹ ⬝ B) = B :=
   mul_nonsing_inv_cancel_left A B (isUnit_det_of_invertible A)
 #align matrix.mul_inv_cancel_left_of_invertible Matrix.mul_inv_cancel_left_of_invertible
 
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 @[simp]
 theorem inv_mul_cancel_right_of_invertible (B : Matrix m n α) [Invertible A] : B ⬝ A⁻¹ ⬝ A = B :=
   nonsing_inv_mul_cancel_right A B (isUnit_det_of_invertible A)
 #align matrix.inv_mul_cancel_right_of_invertible Matrix.inv_mul_cancel_right_of_invertible
 
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 @[simp]
 theorem inv_mul_cancel_left_of_invertible (B : Matrix n m α) [Invertible A] : A⁻¹ ⬝ (A ⬝ B) = B :=
   nonsing_inv_mul_cancel_left A B (isUnit_det_of_invertible A)
 #align matrix.inv_mul_cancel_left_of_invertible Matrix.inv_mul_cancel_left_of_invertible
 
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 theorem inv_mul_eq_iff_eq_mul_of_invertible (A B C : Matrix n n α) [Invertible A] :
     A⁻¹ ⬝ B = C ↔ B = A ⬝ C :=
   ⟨fun h => by rw [← h, mul_inv_cancel_left_of_invertible], fun h => by
     rw [h, inv_mul_cancel_left_of_invertible]⟩
 #align matrix.inv_mul_eq_iff_eq_mul_of_invertible Matrix.inv_mul_eq_iff_eq_mul_of_invertible
 
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 theorem mul_inv_eq_iff_eq_mul_of_invertible (A B C : Matrix n n α) [Invertible A] :
     B ⬝ A⁻¹ = C ↔ B = C ⬝ A :=
   ⟨fun h => by rw [← h, inv_mul_cancel_right_of_invertible], fun h => by
     rw [h, mul_inv_cancel_right_of_invertible]⟩
 #align matrix.mul_inv_eq_iff_eq_mul_of_invertible Matrix.mul_inv_eq_iff_eq_mul_of_invertible
 
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 theorem nonsing_inv_cancel_or_zero : A⁻¹ ⬝ A = 1 ∧ A ⬝ A⁻¹ = 1 ∨ A⁻¹ = 0 :=
   by
   by_cases h : IsUnit A.det
@@ -718,22 +400,10 @@ theorem nonsing_inv_cancel_or_zero : A⁻¹ ⬝ A = 1 ∧ A ⬝ A⁻¹ = 1 ∨ A
   · exact Or.inr (nonsing_inv_apply_not_is_unit _ h)
 #align matrix.nonsing_inv_cancel_or_zero Matrix.nonsing_inv_cancel_or_zero
 
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 theorem det_nonsing_inv_mul_det (h : IsUnit A.det) : A⁻¹.det * A.det = 1 := by
   rw [← det_mul, A.nonsing_inv_mul h, det_one]
 #align matrix.det_nonsing_inv_mul_det Matrix.det_nonsing_inv_mul_det
 
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 @[simp]
 theorem det_nonsing_inv : A⁻¹.det = Ring.inverse A.det :=
   by
@@ -745,22 +415,10 @@ theorem det_nonsing_inv : A⁻¹.det = Ring.inverse A.det :=
   · rw [Ring.inverse_non_unit _ h, nonsing_inv_apply_not_is_unit _ h, det_zero ‹_›]
 #align matrix.det_nonsing_inv Matrix.det_nonsing_inv
 
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 theorem isUnit_nonsing_inv_det (h : IsUnit A.det) : IsUnit A⁻¹.det :=
   isUnit_of_mul_eq_one _ _ (A.det_nonsing_inv_mul_det h)
 #align matrix.is_unit_nonsing_inv_det Matrix.isUnit_nonsing_inv_det
 
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 @[simp]
 theorem nonsing_inv_nonsing_inv (h : IsUnit A.det) : A⁻¹⁻¹ = A :=
   calc
@@ -771,22 +429,10 @@ theorem nonsing_inv_nonsing_inv (h : IsUnit A.det) : A⁻¹⁻¹ = A :=
     
 #align matrix.nonsing_inv_nonsing_inv Matrix.nonsing_inv_nonsing_inv
 
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 theorem isUnit_nonsing_inv_det_iff {A : Matrix n n α} : IsUnit A⁻¹.det ↔ IsUnit A.det := by
   rw [Matrix.det_nonsing_inv, isUnit_ring_inverse]
 #align matrix.is_unit_nonsing_inv_det_iff Matrix.isUnit_nonsing_inv_det_iff
 
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 -- `is_unit.invertible` lifts the proposition `is_unit A` to a constructive inverse of `A`.
 /-- A version of `matrix.invertible_of_det_invertible` with the inverse defeq to `A⁻¹` that is
 therefore noncomputable. -/
@@ -794,48 +440,24 @@ noncomputable def invertibleOfIsUnitDet (h : IsUnit A.det) : Invertible A :=
   ⟨A⁻¹, nonsing_inv_mul A h, mul_nonsing_inv A h⟩
 #align matrix.invertible_of_is_unit_det Matrix.invertibleOfIsUnitDet
 
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 /-- A version of `matrix.units_of_det_invertible` with the inverse defeq to `A⁻¹` that is therefore
 noncomputable. -/
 noncomputable def nonsingInvUnit (h : IsUnit A.det) : (Matrix n n α)ˣ :=
   @unitOfInvertible _ _ _ (invertibleOfIsUnitDet A h)
 #align matrix.nonsing_inv_unit Matrix.nonsingInvUnit
 
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 theorem unitOfDetInvertible_eq_nonsingInvUnit [Invertible A.det] :
     unitOfDetInvertible A = nonsingInvUnit A (isUnit_of_invertible _) := by ext; rfl
 #align matrix.unit_of_det_invertible_eq_nonsing_inv_unit Matrix.unitOfDetInvertible_eq_nonsingInvUnit
 
 variable {A} {B}
 
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 /-- If matrix A is left invertible, then its inverse equals its left inverse. -/
 theorem inv_eq_left_inv (h : B ⬝ A = 1) : A⁻¹ = B :=
   letI := invertible_of_left_inverse _ _ h
   inv_of_eq_nonsing_inv A ▸ invOf_eq_left_inv h
 #align matrix.inv_eq_left_inv Matrix.inv_eq_left_inv
 
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 /-- If matrix A is right invertible, then its inverse equals its right inverse. -/
 theorem inv_eq_right_inv (h : A ⬝ B = 1) : A⁻¹ = B :=
   inv_eq_left_inv (mul_eq_one_comm.2 h)
@@ -845,45 +467,21 @@ section InvEqInv
 
 variable {C : Matrix n n α}
 
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 /-- The left inverse of matrix A is unique when existing. -/
 theorem left_inv_eq_left_inv (h : B ⬝ A = 1) (g : C ⬝ A = 1) : B = C := by
   rw [← inv_eq_left_inv h, ← inv_eq_left_inv g]
 #align matrix.left_inv_eq_left_inv Matrix.left_inv_eq_left_inv
 
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 /-- The right inverse of matrix A is unique when existing. -/
 theorem right_inv_eq_right_inv (h : A ⬝ B = 1) (g : A ⬝ C = 1) : B = C := by
   rw [← inv_eq_right_inv h, ← inv_eq_right_inv g]
 #align matrix.right_inv_eq_right_inv Matrix.right_inv_eq_right_inv
 
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 /-- The right inverse of matrix A equals the left inverse of A when they exist. -/
 theorem right_inv_eq_left_inv (h : A ⬝ B = 1) (g : C ⬝ A = 1) : B = C := by
   rw [← inv_eq_right_inv h, ← inv_eq_left_inv g]
 #align matrix.right_inv_eq_left_inv Matrix.right_inv_eq_left_inv
 
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 theorem inv_inj (h : A⁻¹ = B⁻¹) (h' : IsUnit A.det) : A = B :=
   by
   refine' left_inv_eq_left_inv (mul_nonsing_inv _ h') _
@@ -896,12 +494,6 @@ end InvEqInv
 
 variable (A)
 
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 @[simp]
 theorem inv_zero : (0 : Matrix n n α)⁻¹ = 0 :=
   by
@@ -920,32 +512,14 @@ theorem inv_zero : (0 : Matrix n n α)⁻¹ = 0 :=
 noncomputable instance : InvOneClass (Matrix n n α) :=
   { Matrix.hasOne, Matrix.hasInv with inv_one := inv_eq_left_inv (by simp) }
 
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 theorem inv_smul (k : α) [Invertible k] (h : IsUnit A.det) : (k • A)⁻¹ = ⅟ k • A⁻¹ :=
   inv_eq_left_inv (by simp [h, smul_smul])
 #align matrix.inv_smul Matrix.inv_smul
 
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 theorem inv_smul' (k : αˣ) (h : IsUnit A.det) : (k • A)⁻¹ = k⁻¹ • A⁻¹ :=
   inv_eq_left_inv (by simp [h, smul_smul])
 #align matrix.inv_smul' Matrix.inv_smul'
 
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 theorem inv_adjugate (A : Matrix n n α) (h : IsUnit A.det) : (adjugate A)⁻¹ = h.Unit⁻¹ • A :=
   by
   refine' inv_eq_left_inv _
@@ -954,24 +528,12 @@ theorem inv_adjugate (A : Matrix n n α) (h : IsUnit A.det) : (adjugate A)⁻¹
 
 section Diagonal
 
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 /-- `diagonal v` is invertible if `v` is -/
 def diagonalInvertible {α} [NonAssocSemiring α] (v : n → α) [Invertible v] :
     Invertible (diagonal v) :=
   Invertible.map (diagonalRingHom n α) v
 #align matrix.diagonal_invertible Matrix.diagonalInvertible
 
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 theorem invOf_diagonal_eq {α} [Semiring α] (v : n → α) [Invertible v] [Invertible (diagonal v)] :
     ⅟ (diagonal v) = diagonal (⅟ v) :=
   by
@@ -980,12 +542,6 @@ theorem invOf_diagonal_eq {α} [Semiring α] (v : n → α) [Invertible v] [Inve
   convert(rfl : ⅟ (diagonal v) = _)
 #align matrix.inv_of_diagonal_eq Matrix.invOf_diagonal_eq
 
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-Case conversion may be inaccurate. Consider using '#align matrix.invertible_of_diagonal_invertible Matrix.invertibleOfDiagonalInvertibleₓ'. -/
 /-- `v` is invertible if `diagonal v` is -/
 def invertibleOfDiagonalInvertible (v : n → α) [Invertible (diagonal v)] : Invertible v
     where
@@ -1008,12 +564,6 @@ def invertibleOfDiagonalInvertible (v : n → α) [Invertible (diagonal v)] : In
       exact mul_invOf_self _
 #align matrix.invertible_of_diagonal_invertible Matrix.invertibleOfDiagonalInvertible
 
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-Case conversion may be inaccurate. Consider using '#align matrix.diagonal_invertible_equiv_invertible Matrix.diagonalInvertibleEquivInvertibleₓ'. -/
 /-- Together `matrix.diagonal_invertible` and `matrix.invertible_of_diagonal_invertible` form an
 equivalence, although both sides of the equiv are subsingleton anyway. -/
 @[simps]
@@ -1025,12 +575,6 @@ def diagonalInvertibleEquivInvertible (v : n → α) : Invertible (diagonal v) 
   right_inv _ := Subsingleton.elim _ _
 #align matrix.diagonal_invertible_equiv_invertible Matrix.diagonalInvertibleEquivInvertible
 
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 /-- When lowered to a prop, `matrix.diagonal_invertible_equiv_invertible` forms an `iff`. -/
 @[simp]
 theorem isUnit_diagonal {v : n → α} : IsUnit (diagonal v) ↔ IsUnit v := by
@@ -1038,12 +582,6 @@ theorem isUnit_diagonal {v : n → α} : IsUnit (diagonal v) ↔ IsUnit v := by
     (diagonal_invertible_equiv_invertible v).nonempty_congr]
 #align matrix.is_unit_diagonal Matrix.isUnit_diagonal
 
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 theorem inv_diagonal (v : n → α) : (diagonal v)⁻¹ = diagonal (Ring.inverse v) :=
   by
   rw [nonsing_inv_eq_ring_inverse]
@@ -1058,12 +596,6 @@ theorem inv_diagonal (v : n → α) : (diagonal v)⁻¹ = diagonal (Ring.inverse
 
 end Diagonal
 
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 @[simp]
 theorem inv_inv_inv (A : Matrix n n α) : A⁻¹⁻¹⁻¹ = A⁻¹ :=
   by
@@ -1072,12 +604,6 @@ theorem inv_inv_inv (A : Matrix n n α) : A⁻¹⁻¹⁻¹ = A⁻¹ :=
   · simp [nonsing_inv_apply_not_is_unit _ h]
 #align matrix.inv_inv_inv Matrix.inv_inv_inv
 
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 theorem mul_inv_rev (A B : Matrix n n α) : (A ⬝ B)⁻¹ = B⁻¹ ⬝ A⁻¹ :=
   by
   simp only [inv_def]
@@ -1085,12 +611,6 @@ theorem mul_inv_rev (A B : Matrix n n α) : (A ⬝ B)⁻¹ = B⁻¹ ⬝ A⁻¹ :
     Ring.mul_inverse_rev]
 #align matrix.mul_inv_rev Matrix.mul_inv_rev
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- A version of `list.prod_inv_reverse` for `matrix.has_inv`. -/
 theorem list_prod_inv_reverse : ∀ l : List (Matrix n n α), l.Prod⁻¹ = (l.reverse.map Inv.inv).Prod
@@ -1100,9 +620,6 @@ theorem list_prod_inv_reverse : ∀ l : List (Matrix n n α), l.Prod⁻¹ = (l.r
       Matrix.mul_eq_mul, mul_inv_rev, list_prod_inv_reverse]
 #align matrix.list_prod_inv_reverse Matrix.list_prod_inv_reverse
 
-/- warning: matrix.det_smul_inv_mul_vec_eq_cramer -> Matrix.det_smul_inv_mulVec_eq_cramer is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align matrix.det_smul_inv_mul_vec_eq_cramer Matrix.det_smul_inv_mulVec_eq_cramerₓ'. -/
 /-- One form of **Cramer's rule**. See `matrix.mul_vec_cramer` for a stronger form. -/
 @[simp]
 theorem det_smul_inv_mulVec_eq_cramer (A : Matrix n n α) (b : n → α) (h : IsUnit A.det) :
@@ -1111,9 +628,6 @@ theorem det_smul_inv_mulVec_eq_cramer (A : Matrix n n α) (b : n → α) (h : Is
     h.mul_coe_inv, one_smul]
 #align matrix.det_smul_inv_mul_vec_eq_cramer Matrix.det_smul_inv_mulVec_eq_cramer
 
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-<too large>
-Case conversion may be inaccurate. Consider using '#align matrix.det_smul_inv_vec_mul_eq_cramer_transpose Matrix.det_smul_inv_vecMul_eq_cramer_transposeₓ'. -/
 /-- One form of **Cramer's rule**. See `matrix.mul_vec_cramer` for a stronger form. -/
 @[simp]
 theorem det_smul_inv_vecMul_eq_cramer_transpose (A : Matrix n n α) (b : n → α) (h : IsUnit A.det) :
@@ -1135,12 +649,6 @@ variable [Fintype m]
 
 variable [DecidableEq m]
 
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 /-- `A.submatrix e₁ e₂` is invertible if `A` is -/
 def submatrixEquivInvertible (A : Matrix m m α) (e₁ e₂ : n ≃ m) [Invertible A] :
     Invertible (A.submatrix e₁ e₂) :=
@@ -1148,12 +656,6 @@ def submatrixEquivInvertible (A : Matrix m m α) (e₁ e₂ : n ≃ m) [Invertib
     rw [Matrix.submatrix_mul_equiv, Matrix.mul_invOf_self, submatrix_one_equiv]
 #align matrix.submatrix_equiv_invertible Matrix.submatrixEquivInvertible
 
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 /-- `A` is invertible if `A.submatrix e₁ e₂` is -/
 def invertibleOfSubmatrixEquivInvertible (A : Matrix m m α) (e₁ e₂ : n ≃ m)
     [Invertible (A.submatrix e₁ e₂)] : Invertible A :=
@@ -1166,9 +668,6 @@ def invertibleOfSubmatrixEquivInvertible (A : Matrix m m α) (e₁ e₂ : n ≃
     rw [Matrix.submatrix_mul_equiv, Matrix.mul_invOf_self, submatrix_one_equiv]
 #align matrix.invertible_of_submatrix_equiv_invertible Matrix.invertibleOfSubmatrixEquivInvertible
 
-/- warning: matrix.inv_of_submatrix_equiv_eq -> Matrix.invOf_submatrix_equiv_eq is a dubious translation:
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 theorem invOf_submatrix_equiv_eq (A : Matrix m m α) (e₁ e₂ : n ≃ m) [Invertible A]
     [Invertible (A.submatrix e₁ e₂)] : ⅟ (A.submatrix e₁ e₂) = (⅟ A).submatrix e₂ e₁ :=
   by
@@ -1177,12 +676,6 @@ theorem invOf_submatrix_equiv_eq (A : Matrix m m α) (e₁ e₂ : n ≃ m) [Inve
   convert(rfl : ⅟ (A.submatrix e₁ e₂) = _)
 #align matrix.inv_of_submatrix_equiv_eq Matrix.invOf_submatrix_equiv_eq
 
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 /-- Together `matrix.submatrix_equiv_invertible` and
 `matrix.invertible_of_submatrix_equiv_invertible` form an equivalence, although both sides of the
 equiv are subsingleton anyway. -/
@@ -1206,12 +699,6 @@ theorem isUnit_submatrix_equiv {A : Matrix m m α} (e₁ e₂ : n ≃ m) :
 #align matrix.is_unit_submatrix_equiv Matrix.isUnit_submatrix_equiv
 -/
 
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 @[simp]
 theorem inv_submatrix_equiv (A : Matrix m m α) (e₁ e₂ : n ≃ m) :
     (A.submatrix e₁ e₂)⁻¹ = A⁻¹.submatrix e₂ e₁ :=
@@ -1225,12 +712,6 @@ theorem inv_submatrix_equiv (A : Matrix m m α) (e₁ e₂ : n ≃ m) :
       submatrix_zero, Pi.zero_apply]
 #align matrix.inv_submatrix_equiv Matrix.inv_submatrix_equiv
 
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 theorem inv_reindex (e₁ e₂ : n ≃ m) (A : Matrix n n α) : (reindex e₁ e₂ A)⁻¹ = reindex e₂ e₁ A⁻¹ :=
   inv_submatrix_equiv A e₁.symm e₂.symm
 #align matrix.inv_reindex Matrix.inv_reindex
@@ -1244,23 +725,11 @@ section Det
 
 variable [Fintype m] [DecidableEq m]
 
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 /-- A variant of `matrix.det_units_conj`. -/
 theorem det_conj {M : Matrix m m α} (h : IsUnit M) (N : Matrix m m α) : det (M ⬝ N ⬝ M⁻¹) = det N :=
   by rw [← h.unit_spec, ← coe_units_inv, det_units_conj]
 #align matrix.det_conj Matrix.det_conj
 
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 /-- A variant of `matrix.det_units_conj'`. -/
 theorem det_conj' {M : Matrix m m α} (h : IsUnit M) (N : Matrix m m α) :
     det (M⁻¹ ⬝ N ⬝ M) = det N := by rw [← h.unit_spec, ← coe_units_inv, det_units_conj']

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -162,10 +162,8 @@ lean 3 declaration is
 but is expected to have type
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{u2} α (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)] [_inst_5 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) A], Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Invertible.invOf.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) A _inst_5) (HSMul.hSMul.{u2, max u1 u2, max u1 u2} α (Matrix.{u1, u1, u2} n n α) (Matrix.{u1, u1, u2} n n α) (instHSMul.{u2, max u1 u2} α (Matrix.{u1, u1, u2} n n α) (Matrix.smul.{u2, u1, u1, u2} n n α α (Algebra.toSMul.{u2, u2} α α (CommRing.toCommSemiring.{u2} α _inst_3) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (Algebra.id.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Invertible.invOf.{u2} α (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) _inst_4) (Matrix.adjugate.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 A))
 Case conversion may be inaccurate. Consider using '#align matrix.inv_of_eq Matrix.invOf_eqₓ'. -/
-theorem invOf_eq [Invertible A.det] [Invertible A] : ⅟ A = ⅟ A.det • A.adjugate :=
-  by
-  letI := invertible_of_det_invertible A
-  convert(rfl : ⅟ A = _)
+theorem invOf_eq [Invertible A.det] [Invertible A] : ⅟ A = ⅟ A.det • A.adjugate := by
+  letI := invertible_of_det_invertible A; convert(rfl : ⅟ A = _)
 #align matrix.inv_of_eq Matrix.invOf_eq
 
 /- warning: matrix.det_invertible_of_left_inverse -> Matrix.detInvertibleOfLeftInverse is a dubious translation:
@@ -213,10 +211,8 @@ lean 3 declaration is
 but is expected to have type
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) A] [_inst_5 : Invertible.{u2} α (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)], Eq.{succ u2} α (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 (Invertible.invOf.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) A _inst_4)) (Invertible.invOf.{u2} α (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) _inst_5)
 Case conversion may be inaccurate. Consider using '#align matrix.det_inv_of Matrix.det_invOfₓ'. -/
-theorem det_invOf [Invertible A] [Invertible A.det] : (⅟ A).det = ⅟ A.det :=
-  by
-  letI := det_invertible_of_invertible A
-  convert(rfl : _ = ⅟ A.det)
+theorem det_invOf [Invertible A] [Invertible A.det] : (⅟ A).det = ⅟ A.det := by
+  letI := det_invertible_of_invertible A; convert(rfl : _ = ⅟ A.det)
 #align matrix.det_inv_of Matrix.det_invOf
 
 /- warning: matrix.invertible_equiv_det_invertible -> Matrix.invertibleEquivDetInvertible is a dubious translation:
@@ -428,10 +424,7 @@ lean 3 declaration is
 but is expected to have type
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 (Matrix.transpose.{u2, u1, u1} n n α A)))
 Case conversion may be inaccurate. Consider using '#align matrix.is_unit_det_transpose Matrix.isUnit_det_transposeₓ'. -/
-theorem isUnit_det_transpose (h : IsUnit A.det) : IsUnit Aᵀ.det :=
-  by
-  rw [det_transpose]
-  exact h
+theorem isUnit_det_transpose (h : IsUnit A.det) : IsUnit Aᵀ.det := by rw [det_transpose]; exact h
 #align matrix.is_unit_det_transpose Matrix.isUnit_det_transpose
 
 /-! ### A noncomputable `has_inv` instance  -/
@@ -565,10 +558,7 @@ theorem nonsing_inv_mul (h : IsUnit A.det) : A⁻¹ ⬝ A = 1 :=
   rw [← inv_of_eq_nonsing_inv, Matrix.invOf_mul_self]
 #align matrix.nonsing_inv_mul Matrix.nonsing_inv_mul
 
-instance [Invertible A] : Invertible A⁻¹ :=
-  by
-  rw [← inv_of_eq_nonsing_inv]
-  infer_instance
+instance [Invertible A] : Invertible A⁻¹ := by rw [← inv_of_eq_nonsing_inv]; infer_instance
 
 /- warning: matrix.inv_inv_of_invertible -> Matrix.inv_inv_of_invertible is a dubious translation:
 lean 3 declaration is
@@ -748,8 +738,7 @@ Case conversion may be inaccurate. Consider using '#align matrix.det_nonsing_inv
 theorem det_nonsing_inv : A⁻¹.det = Ring.inverse A.det :=
   by
   by_cases h : IsUnit A.det
-  · cases h.nonempty_invertible
-    letI := invertible_of_det_invertible A
+  · cases h.nonempty_invertible; letI := invertible_of_det_invertible A
     rw [Ring.inverse_invertible, ← inv_of_eq_nonsing_inv, det_inv_of]
   cases isEmpty_or_nonempty n
   · rw [det_is_empty, det_is_empty, Ring.inverse_one]
@@ -824,10 +813,7 @@ but is expected to have type
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{u2} α (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)], Eq.{max (succ u1) (succ u2)} (Units.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_1 (fun (a : n) (b : n) => _inst_2 a b))))) (Matrix.unitOfDetInvertible.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3 A _inst_4) (Matrix.nonsingInvUnit.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3 A (isUnit_of_invertible.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) _inst_4))
 Case conversion may be inaccurate. Consider using '#align matrix.unit_of_det_invertible_eq_nonsing_inv_unit Matrix.unitOfDetInvertible_eq_nonsingInvUnitₓ'. -/
 theorem unitOfDetInvertible_eq_nonsingInvUnit [Invertible A.det] :
-    unitOfDetInvertible A = nonsingInvUnit A (isUnit_of_invertible _) :=
-  by
-  ext
-  rfl
+    unitOfDetInvertible A = nonsingInvUnit A (isUnit_of_invertible _) := by ext; rfl
 #align matrix.unit_of_det_invertible_eq_nonsing_inv_unit Matrix.unitOfDetInvertible_eq_nonsingInvUnit
 
 variable {A} {B}

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -1115,10 +1115,7 @@ theorem list_prod_inv_reverse : ∀ l : List (Matrix n n α), l.Prod⁻¹ = (l.r
 #align matrix.list_prod_inv_reverse Matrix.list_prod_inv_reverse
 
 /- warning: matrix.det_smul_inv_mul_vec_eq_cramer -> Matrix.det_smul_inv_mulVec_eq_cramer is a dubious translation:
-lean 3 declaration is
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (b : n -> α), (IsUnit.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{succ (max u1 u2)} (n -> α) (SMul.smul.{u2, max u1 u2} α (n -> α) (Function.hasSMul.{u1, u2, u2} n α α (Mul.toSMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) (Matrix.mulVec.{u2, u1, u1} n n α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) _inst_1 (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) b)) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u2, u2, max u1 u2, max u1 u2} α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (n -> α) (n -> α) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.Function.module.{u1, u2, u2} n α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Pi.Function.module.{u1, u2, u2} n α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (_x : LinearMap.{u2, u2, max u1 u2, max u1 u2} α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (n -> α) (n -> α) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.Function.module.{u1, u2, u2} n α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Pi.Function.module.{u1, u2, u2} n α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) => (n -> α) -> n -> α) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, max u1 u2} α α (n -> α) (n -> α) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.Function.module.{u1, u2, u2} n α α (Ring.toSemiring.{u2} α 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 Case conversion may be inaccurate. Consider using '#align matrix.det_smul_inv_mul_vec_eq_cramer Matrix.det_smul_inv_mulVec_eq_cramerₓ'. -/
 /-- One form of **Cramer's rule**. See `matrix.mul_vec_cramer` for a stronger form. -/
 @[simp]
@@ -1129,10 +1126,7 @@ theorem det_smul_inv_mulVec_eq_cramer (A : Matrix n n α) (b : n → α) (h : Is
 #align matrix.det_smul_inv_mul_vec_eq_cramer Matrix.det_smul_inv_mulVec_eq_cramer
 
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(fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Matrix.cramer.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 (Matrix.transpose.{u2, u1, u1} n n α A)) b))
+<too large>
 Case conversion may be inaccurate. Consider using '#align matrix.det_smul_inv_vec_mul_eq_cramer_transpose Matrix.det_smul_inv_vecMul_eq_cramer_transposeₓ'. -/
 /-- One form of **Cramer's rule**. See `matrix.mul_vec_cramer` for a stronger form. -/
 @[simp]
@@ -1187,10 +1181,7 @@ def invertibleOfSubmatrixEquivInvertible (A : Matrix m m α) (e₁ e₂ : n ≃
 #align matrix.invertible_of_submatrix_equiv_invertible Matrix.invertibleOfSubmatrixEquivInvertible
 
 /- warning: matrix.inv_of_submatrix_equiv_eq -> Matrix.invOf_submatrix_equiv_eq is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align matrix.inv_of_submatrix_equiv_eq Matrix.invOf_submatrix_equiv_eqₓ'. -/
 theorem invOf_submatrix_equiv_eq (A : Matrix m m α) (e₁ e₂ : n ≃ m) [Invertible A]
     [Invertible (A.submatrix e₁ e₂)] : ⅟ (A.submatrix e₁ e₂) = (⅟ A).submatrix e₂ e₁ :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b

@@ -1118,7 +1118,7 @@ theorem list_prod_inv_reverse : ∀ l : List (Matrix n n α), l.Prod⁻¹ = (l.r
 lean 3 declaration is
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(CommRing.toRing.{u2} α _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Pi.Function.module.{u1, u2, u2} n α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.cramer.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 A) b))
 but is expected to have type
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(NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (n -> α) (fun (_x : n -> α) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : n -> α) => n -> α) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, max u1 u2} α α (n -> α) (n -> α) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Matrix.cramer.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 A) b))
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (b : n -> α), (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{max (succ u1) (succ u2)} (n -> α) (HSMul.hSMul.{u2, max u1 u2, max u1 u2} α (n -> α) (n -> α) (instHSMul.{u2, max u1 u2} α (n -> α) (Pi.instSMul.{u1, u2, u2} n α (fun (a._@.Mathlib.Data.Matrix.Basic._hyg.18074 : n) => α) (fun (i : n) => Algebra.toSMul.{u2, u2} α α (CommRing.toCommSemiring.{u2} α _inst_3) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (Algebra.id.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) (Matrix.mulVec.{u2, u1, u1} n n α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) _inst_1 (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) b)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u2, u2, max u1 u2, max u1 u2} α α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (n -> α) (n -> α) (Pi.addCommMonoid.{u1, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (n -> α) (fun (_x : n -> α) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : n -> α) => n -> α) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, max u1 u2} α α (n -> α) (n -> α) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Matrix.cramer.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 A) b))
 Case conversion may be inaccurate. Consider using '#align matrix.det_smul_inv_mul_vec_eq_cramer Matrix.det_smul_inv_mulVec_eq_cramerₓ'. -/
 /-- One form of **Cramer's rule**. See `matrix.mul_vec_cramer` for a stronger form. -/
 @[simp]
@@ -1132,7 +1132,7 @@ theorem det_smul_inv_mulVec_eq_cramer (A : Matrix n n α) (b : n → α) (h : Is
 lean 3 declaration is
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 but is expected to have type
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(fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Matrix.cramer.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 (Matrix.transpose.{u2, u1, u1} n n α A)) b))
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(NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (n -> α) (fun (_x : n -> α) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : n -> α) => n -> α) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, max u1 u2} α α (n -> α) (n -> α) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Matrix.cramer.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 (Matrix.transpose.{u2, u1, u1} n n α A)) b))
 Case conversion may be inaccurate. Consider using '#align matrix.det_smul_inv_vec_mul_eq_cramer_transpose Matrix.det_smul_inv_vecMul_eq_cramer_transposeₓ'. -/
 /-- One form of **Cramer's rule**. See `matrix.mul_vec_cramer` for a stronger form. -/
 @[simp]

mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4

@@ -1159,7 +1159,7 @@ variable [DecidableEq m]
 lean 3 declaration is
   forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] [_inst_4 : Fintype.{u1} m] [_inst_5 : DecidableEq.{succ u1} m] (A : Matrix.{u1, u1, u3} m m α) (e₁ : Equiv.{succ u2, succ u1} n m) (e₂ : Equiv.{succ u2, succ u1} n m) [_inst_6 : Invertible.{max u1 u3} (Matrix.{u1, u1, u3} m m α) (Matrix.hasMul.{u3, u1} m α _inst_4 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.hasOne.{u3, u1} m α (fun (a : m) (b : m) => _inst_5 a b) (MulZeroClass.toHasZero.{u3} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (AddMonoidWithOne.toOne.{u3} α (AddGroupWithOne.toAddMonoidWithOne.{u3} α (AddCommGroupWithOne.toAddGroupWithOne.{u3} α (Ring.toAddCommGroupWithOne.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) A], Invertible.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.hasMul.{u3, u2} n α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.hasOne.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u3} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (AddMonoidWithOne.toOne.{u3} α (AddGroupWithOne.toAddMonoidWithOne.{u3} α (AddCommGroupWithOne.toAddGroupWithOne.{u3} α (Ring.toAddCommGroupWithOne.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.submatrix.{u3, u2, u1, u1, u2} n m m n α A (coeFn.{max 1 (max (succ u2) (succ u1)) (succ u1) (succ u2), max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} n m) (fun (_x : Equiv.{succ u2, succ u1} n m) => n -> m) (Equiv.hasCoeToFun.{succ u2, succ u1} n m) e₁) (coeFn.{max 1 (max (succ u2) (succ u1)) (succ u1) (succ u2), max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} n m) (fun (_x : Equiv.{succ u2, succ u1} n m) => n -> m) (Equiv.hasCoeToFun.{succ u2, succ u1} n m) e₂))
 but is expected to have type
-  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] [_inst_4 : Fintype.{u1} m] [_inst_5 : DecidableEq.{succ u1} m] (A : Matrix.{u1, u1, u3} m m α) (e₁ : Equiv.{succ u2, succ u1} n m) (e₂ : Equiv.{succ u2, succ u1} n m) [_inst_6 : Invertible.{max u1 u3} (Matrix.{u1, u1, u3} m m α) (Matrix.instMulMatrix.{u3, u1} m α _inst_4 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u1} m α (fun (a : m) (b : m) => _inst_5 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (Semiring.toOne.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) A], Invertible.{max u3 u2} (Matrix.{u2, u2, u3} n n α) (Matrix.instMulMatrix.{u3, u2} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (Semiring.toOne.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) (Matrix.submatrix.{u3, u2, u1, u1, u2} n m m n α A (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₁) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₂))
+  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] [_inst_4 : Fintype.{u1} m] [_inst_5 : DecidableEq.{succ u1} m] (A : Matrix.{u1, u1, u3} m m α) (e₁ : Equiv.{succ u2, succ u1} n m) (e₂ : Equiv.{succ u2, succ u1} n m) [_inst_6 : Invertible.{max u1 u3} (Matrix.{u1, u1, u3} m m α) (Matrix.instMulMatrix.{u3, u1} m α _inst_4 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u1} m α (fun (a : m) (b : m) => _inst_5 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (Semiring.toOne.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) A], Invertible.{max u3 u2} (Matrix.{u2, u2, u3} n n α) (Matrix.instMulMatrix.{u3, u2} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (Semiring.toOne.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) (Matrix.submatrix.{u3, u2, u1, u1, u2} n m m n α A (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₁) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₂))
 Case conversion may be inaccurate. Consider using '#align matrix.submatrix_equiv_invertible Matrix.submatrixEquivInvertibleₓ'. -/
 /-- `A.submatrix e₁ e₂` is invertible if `A` is -/
 def submatrixEquivInvertible (A : Matrix m m α) (e₁ e₂ : n ≃ m) [Invertible A] :
@@ -1172,7 +1172,7 @@ def submatrixEquivInvertible (A : Matrix m m α) (e₁ e₂ : n ≃ m) [Invertib
 lean 3 declaration is
   forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] [_inst_4 : Fintype.{u1} m] [_inst_5 : DecidableEq.{succ u1} m] (A : Matrix.{u1, u1, u3} m m α) (e₁ : Equiv.{succ u2, succ u1} n m) (e₂ : Equiv.{succ u2, succ u1} n m) [_inst_6 : Invertible.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.hasMul.{u3, u2} n α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.hasOne.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u3} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (AddMonoidWithOne.toOne.{u3} α (AddGroupWithOne.toAddMonoidWithOne.{u3} α (AddCommGroupWithOne.toAddGroupWithOne.{u3} α (Ring.toAddCommGroupWithOne.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.submatrix.{u3, u2, u1, u1, u2} n m m n α A (coeFn.{max 1 (max (succ u2) (succ u1)) (succ u1) (succ u2), max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} n m) (fun (_x : Equiv.{succ u2, succ u1} n m) => n -> m) (Equiv.hasCoeToFun.{succ u2, succ u1} n m) e₁) (coeFn.{max 1 (max (succ u2) (succ u1)) (succ u1) (succ u2), max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} n m) (fun (_x : Equiv.{succ u2, succ u1} n m) => n -> m) (Equiv.hasCoeToFun.{succ u2, succ u1} n m) e₂))], Invertible.{max u1 u3} (Matrix.{u1, u1, u3} m m α) (Matrix.hasMul.{u3, u1} m α _inst_4 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.hasOne.{u3, u1} m α (fun (a : m) (b : m) => _inst_5 a b) (MulZeroClass.toHasZero.{u3} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (AddMonoidWithOne.toOne.{u3} α (AddGroupWithOne.toAddMonoidWithOne.{u3} α (AddCommGroupWithOne.toAddGroupWithOne.{u3} α (Ring.toAddCommGroupWithOne.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) A
 but is expected to have type
-  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] [_inst_4 : Fintype.{u1} m] [_inst_5 : DecidableEq.{succ u1} m] (A : Matrix.{u1, u1, u3} m m α) (e₁ : Equiv.{succ u2, succ u1} n m) (e₂ : Equiv.{succ u2, succ u1} n m) [_inst_6 : Invertible.{max u3 u2} (Matrix.{u2, u2, u3} n n α) (Matrix.instMulMatrix.{u3, u2} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (Semiring.toOne.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) (Matrix.submatrix.{u3, u2, u1, u1, u2} n m m n α A (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₁) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₂))], Invertible.{max u1 u3} (Matrix.{u1, u1, u3} m m α) (Matrix.instMulMatrix.{u3, u1} m α _inst_4 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u1} m α (fun (a : m) (b : m) => _inst_5 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (Semiring.toOne.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) A
+  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] [_inst_4 : Fintype.{u1} m] [_inst_5 : DecidableEq.{succ u1} m] (A : Matrix.{u1, u1, u3} m m α) (e₁ : Equiv.{succ u2, succ u1} n m) (e₂ : Equiv.{succ u2, succ u1} n m) [_inst_6 : Invertible.{max u3 u2} (Matrix.{u2, u2, u3} n n α) (Matrix.instMulMatrix.{u3, u2} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (Semiring.toOne.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) (Matrix.submatrix.{u3, u2, u1, u1, u2} n m m n α A (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₁) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₂))], Invertible.{max u1 u3} (Matrix.{u1, u1, u3} m m α) (Matrix.instMulMatrix.{u3, u1} m α _inst_4 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u1} m α (fun (a : m) (b : m) => _inst_5 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (Semiring.toOne.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) A
 Case conversion may be inaccurate. Consider using '#align matrix.invertible_of_submatrix_equiv_invertible Matrix.invertibleOfSubmatrixEquivInvertibleₓ'. -/
 /-- `A` is invertible if `A.submatrix e₁ e₂` is -/
 def invertibleOfSubmatrixEquivInvertible (A : Matrix m m α) (e₁ e₂ : n ≃ m)
@@ -1190,7 +1190,7 @@ def invertibleOfSubmatrixEquivInvertible (A : Matrix m m α) (e₁ e₂ : n ≃
 lean 3 declaration is
   forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] [_inst_4 : Fintype.{u1} m] [_inst_5 : DecidableEq.{succ u1} m] (A : Matrix.{u1, u1, u3} m m α) (e₁ : Equiv.{succ u2, succ u1} n m) (e₂ : Equiv.{succ u2, succ u1} n m) [_inst_6 : Invertible.{max u1 u3} (Matrix.{u1, u1, u3} m m α) (Matrix.hasMul.{u3, u1} m α _inst_4 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.hasOne.{u3, u1} m α (fun (a : m) (b : m) => _inst_5 a b) (MulZeroClass.toHasZero.{u3} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (AddMonoidWithOne.toOne.{u3} α (AddGroupWithOne.toAddMonoidWithOne.{u3} α (AddCommGroupWithOne.toAddGroupWithOne.{u3} α (Ring.toAddCommGroupWithOne.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) A] [_inst_7 : Invertible.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.hasMul.{u3, u2} n α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.hasOne.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u3} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (AddMonoidWithOne.toOne.{u3} α (AddGroupWithOne.toAddMonoidWithOne.{u3} α (AddCommGroupWithOne.toAddGroupWithOne.{u3} α (Ring.toAddCommGroupWithOne.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.submatrix.{u3, u2, u1, u1, u2} n m m n α A (coeFn.{max 1 (max (succ u2) (succ u1)) (succ u1) (succ u2), max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} n m) (fun (_x : Equiv.{succ u2, succ u1} n m) => n -> m) (Equiv.hasCoeToFun.{succ u2, succ u1} n m) e₁) (coeFn.{max 1 (max (succ u2) (succ u1)) (succ u1) (succ u2), max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} n m) (fun (_x : Equiv.{succ u2, succ u1} n m) => n -> m) (Equiv.hasCoeToFun.{succ u2, succ u1} n m) e₂))], Eq.{succ (max u2 u3)} (Matrix.{u2, u2, u3} n n α) (Invertible.invOf.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.hasMul.{u3, u2} n α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.hasOne.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u3} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (AddMonoidWithOne.toOne.{u3} α (AddGroupWithOne.toAddMonoidWithOne.{u3} α (AddCommGroupWithOne.toAddGroupWithOne.{u3} α (Ring.toAddCommGroupWithOne.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.submatrix.{u3, u2, u1, u1, u2} n m m n α A (coeFn.{max 1 (max (succ u2) (succ u1)) (succ u1) (succ u2), max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} n m) (fun (_x : Equiv.{succ u2, succ u1} n m) => n -> m) (Equiv.hasCoeToFun.{succ u2, succ u1} n m) e₁) (coeFn.{max 1 (max (succ u2) (succ u1)) (succ u1) (succ u2), max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} n m) (fun (_x : Equiv.{succ u2, succ u1} n m) => n -> m) (Equiv.hasCoeToFun.{succ u2, succ u1} n m) e₂)) _inst_7) (Matrix.submatrix.{u3, u2, u1, u1, u2} n m m n α (Invertible.invOf.{max u1 u3} (Matrix.{u1, u1, u3} m m α) (Matrix.hasMul.{u3, u1} m α _inst_4 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.hasOne.{u3, u1} m α (fun (a : m) (b : m) => _inst_5 a b) (MulZeroClass.toHasZero.{u3} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (AddMonoidWithOne.toOne.{u3} α (AddGroupWithOne.toAddMonoidWithOne.{u3} α (AddCommGroupWithOne.toAddGroupWithOne.{u3} α (Ring.toAddCommGroupWithOne.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) A _inst_6) (coeFn.{max 1 (max (succ u2) (succ u1)) (succ u1) (succ u2), max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} n m) (fun (_x : Equiv.{succ u2, succ u1} n m) => n -> m) (Equiv.hasCoeToFun.{succ u2, succ u1} n m) e₂) (coeFn.{max 1 (max (succ u2) (succ u1)) (succ u1) (succ u2), max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} n m) (fun (_x : Equiv.{succ u2, succ u1} n m) => n -> m) (Equiv.hasCoeToFun.{succ u2, succ u1} n m) e₁))
 but is expected to have type
-  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] [_inst_4 : Fintype.{u1} m] [_inst_5 : DecidableEq.{succ u1} m] (A : Matrix.{u1, u1, u3} m m α) (e₁ : Equiv.{succ u2, succ u1} n m) (e₂ : Equiv.{succ u2, succ u1} n m) [_inst_6 : Invertible.{max u1 u3} (Matrix.{u1, u1, u3} m m α) (Matrix.instMulMatrix.{u3, u1} m α _inst_4 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u1} m α (fun (a : m) (b : m) => _inst_5 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (Semiring.toOne.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) A] [_inst_7 : Invertible.{max u3 u2} (Matrix.{u2, u2, u3} n n α) (Matrix.instMulMatrix.{u3, u2} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (Semiring.toOne.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) (Matrix.submatrix.{u3, u2, u1, u1, u2} n m m n α A (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₁) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₂))], Eq.{max (succ u2) (succ u3)} (Matrix.{u2, u2, u3} n n α) (Invertible.invOf.{max u3 u2} (Matrix.{u2, u2, u3} n n α) (Matrix.instMulMatrix.{u3, u2} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (Semiring.toOne.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) (Matrix.submatrix.{u3, u2, u1, u1, u2} n m m n α A (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₁) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₂)) _inst_7) (Matrix.submatrix.{u3, u2, u1, u1, u2} n m m n α (Invertible.invOf.{max u1 u3} (Matrix.{u1, u1, u3} m m α) (Matrix.instMulMatrix.{u3, u1} m α _inst_4 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u1} m α (fun (a : m) (b : m) => _inst_5 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (Semiring.toOne.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) A _inst_6) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₂) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₁))
+  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] [_inst_4 : Fintype.{u1} m] [_inst_5 : DecidableEq.{succ u1} m] (A : Matrix.{u1, u1, u3} m m α) (e₁ : Equiv.{succ u2, succ u1} n m) (e₂ : Equiv.{succ u2, succ u1} n m) [_inst_6 : Invertible.{max u1 u3} (Matrix.{u1, u1, u3} m m α) (Matrix.instMulMatrix.{u3, u1} m α _inst_4 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u1} m α (fun (a : m) (b : m) => _inst_5 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (Semiring.toOne.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) A] [_inst_7 : Invertible.{max u3 u2} (Matrix.{u2, u2, u3} n n α) (Matrix.instMulMatrix.{u3, u2} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (Semiring.toOne.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) (Matrix.submatrix.{u3, u2, u1, u1, u2} n m m n α A (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₁) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₂))], Eq.{max (succ u2) (succ u3)} (Matrix.{u2, u2, u3} n n α) (Invertible.invOf.{max u3 u2} (Matrix.{u2, u2, u3} n n α) (Matrix.instMulMatrix.{u3, u2} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (Semiring.toOne.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) (Matrix.submatrix.{u3, u2, u1, u1, u2} n m m n α A (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₁) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₂)) _inst_7) (Matrix.submatrix.{u3, u2, u1, u1, u2} n m m n α (Invertible.invOf.{max u1 u3} (Matrix.{u1, u1, u3} m m α) (Matrix.instMulMatrix.{u3, u1} m α _inst_4 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u1} m α (fun (a : m) (b : m) => _inst_5 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (Semiring.toOne.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) A _inst_6) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₂) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₁))
 Case conversion may be inaccurate. Consider using '#align matrix.inv_of_submatrix_equiv_eq Matrix.invOf_submatrix_equiv_eqₓ'. -/
 theorem invOf_submatrix_equiv_eq (A : Matrix m m α) (e₁ e₂ : n ≃ m) [Invertible A]
     [Invertible (A.submatrix e₁ e₂)] : ⅟ (A.submatrix e₁ e₂) = (⅟ A).submatrix e₂ e₁ :=
@@ -1204,7 +1204,7 @@ theorem invOf_submatrix_equiv_eq (A : Matrix m m α) (e₁ e₂ : n ≃ m) [Inve
 lean 3 declaration is
   forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] [_inst_4 : Fintype.{u1} m] [_inst_5 : DecidableEq.{succ u1} m] (A : Matrix.{u1, u1, u3} m m α) (e₁ : Equiv.{succ u2, succ u1} n m) (e₂ : Equiv.{succ u2, succ u1} n m), Equiv.{succ (max u2 u3), succ (max u1 u3)} (Invertible.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.hasMul.{u3, u2} n α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.hasOne.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u3} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (AddMonoidWithOne.toOne.{u3} α (AddGroupWithOne.toAddMonoidWithOne.{u3} α (AddCommGroupWithOne.toAddGroupWithOne.{u3} α (Ring.toAddCommGroupWithOne.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.submatrix.{u3, u2, u1, u1, u2} n m m n α A (coeFn.{max 1 (max (succ u2) (succ u1)) (succ u1) (succ u2), max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} n m) (fun (_x : Equiv.{succ u2, succ u1} n m) => n -> m) (Equiv.hasCoeToFun.{succ u2, succ u1} n m) e₁) (coeFn.{max 1 (max (succ u2) (succ u1)) (succ u1) (succ u2), max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} n m) (fun (_x : Equiv.{succ u2, succ u1} n m) => n -> m) (Equiv.hasCoeToFun.{succ u2, succ u1} n m) e₂))) (Invertible.{max u1 u3} (Matrix.{u1, u1, u3} m m α) (Matrix.hasMul.{u3, u1} m α _inst_4 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.hasOne.{u3, u1} m α (fun (a : m) (b : m) => _inst_5 a b) (MulZeroClass.toHasZero.{u3} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (AddMonoidWithOne.toOne.{u3} α (AddGroupWithOne.toAddMonoidWithOne.{u3} α (AddCommGroupWithOne.toAddGroupWithOne.{u3} α (Ring.toAddCommGroupWithOne.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) A)
 but is expected to have type
-  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] [_inst_4 : Fintype.{u1} m] [_inst_5 : DecidableEq.{succ u1} m] (A : Matrix.{u1, u1, u3} m m α) (e₁ : Equiv.{succ u2, succ u1} n m) (e₂ : Equiv.{succ u2, succ u1} n m), Equiv.{succ (max u3 u2), succ (max u1 u3)} (Invertible.{max u3 u2} (Matrix.{u2, u2, u3} n n α) (Matrix.instMulMatrix.{u3, u2} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (Semiring.toOne.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) (Matrix.submatrix.{u3, u2, u1, u1, u2} n m m n α A (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₁) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₂))) (Invertible.{max u1 u3} (Matrix.{u1, u1, u3} m m α) (Matrix.instMulMatrix.{u3, u1} m α _inst_4 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u1} m α (fun (a : m) (b : m) => _inst_5 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (Semiring.toOne.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) A)
+  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] [_inst_4 : Fintype.{u1} m] [_inst_5 : DecidableEq.{succ u1} m] (A : Matrix.{u1, u1, u3} m m α) (e₁ : Equiv.{succ u2, succ u1} n m) (e₂ : Equiv.{succ u2, succ u1} n m), Equiv.{succ (max u3 u2), succ (max u1 u3)} (Invertible.{max u3 u2} (Matrix.{u2, u2, u3} n n α) (Matrix.instMulMatrix.{u3, u2} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (Semiring.toOne.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) (Matrix.submatrix.{u3, u2, u1, u1, u2} n m m n α A (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₁) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₂))) (Invertible.{max u1 u3} (Matrix.{u1, u1, u3} m m α) (Matrix.instMulMatrix.{u3, u1} m α _inst_4 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u1} m α (fun (a : m) (b : m) => _inst_5 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (Semiring.toOne.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) A)
 Case conversion may be inaccurate. Consider using '#align matrix.submatrix_equiv_invertible_equiv_invertible Matrix.submatrixEquivInvertibleEquivInvertibleₓ'. -/
 /-- Together `matrix.submatrix_equiv_invertible` and
 `matrix.invertible_of_submatrix_equiv_invertible` form an equivalence, although both sides of the
@@ -1233,7 +1233,7 @@ theorem isUnit_submatrix_equiv {A : Matrix m m α} (e₁ e₂ : n ≃ m) :
 lean 3 declaration is
   forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] [_inst_4 : Fintype.{u1} m] [_inst_5 : DecidableEq.{succ u1} m] (A : Matrix.{u1, u1, u3} m m α) (e₁ : Equiv.{succ u2, succ u1} n m) (e₂ : Equiv.{succ u2, succ u1} n m), Eq.{succ (max u2 u3)} (Matrix.{u2, u2, u3} n n α) (Inv.inv.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.hasInv.{u2, u3} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) (Matrix.submatrix.{u3, u2, u1, u1, u2} n m m n α A (coeFn.{max 1 (max (succ u2) (succ u1)) (succ u1) (succ u2), max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} n m) (fun (_x : Equiv.{succ u2, succ u1} n m) => n -> m) (Equiv.hasCoeToFun.{succ u2, succ u1} n m) e₁) (coeFn.{max 1 (max (succ u2) (succ u1)) (succ u1) (succ u2), max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} n m) (fun (_x : Equiv.{succ u2, succ u1} n m) => n -> m) (Equiv.hasCoeToFun.{succ u2, succ u1} n m) e₂))) (Matrix.submatrix.{u3, u2, u1, u1, u2} n m m n α (Inv.inv.{max u1 u3} (Matrix.{u1, u1, u3} m m α) (Matrix.hasInv.{u1, u3} m α _inst_4 (fun (a : m) (b : m) => _inst_5 a b) _inst_3) A) (coeFn.{max 1 (max (succ u2) (succ u1)) (succ u1) (succ u2), max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} n m) (fun (_x : Equiv.{succ u2, succ u1} n m) => n -> m) (Equiv.hasCoeToFun.{succ u2, succ u1} n m) e₂) (coeFn.{max 1 (max (succ u2) (succ u1)) (succ u1) (succ u2), max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} n m) (fun (_x : Equiv.{succ u2, succ u1} n m) => n -> m) (Equiv.hasCoeToFun.{succ u2, succ u1} n m) e₁))
 but is expected to have type
-  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] [_inst_4 : Fintype.{u1} m] [_inst_5 : DecidableEq.{succ u1} m] (A : Matrix.{u1, u1, u3} m m α) (e₁ : Equiv.{succ u2, succ u1} n m) (e₂ : Equiv.{succ u2, succ u1} n m), Eq.{max (succ u2) (succ u3)} (Matrix.{u2, u2, u3} n n α) (Inv.inv.{max u3 u2} (Matrix.{u2, u2, u3} n n α) (Matrix.inv.{u2, u3} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) (Matrix.submatrix.{u3, u2, u1, u1, u2} n m m n α A (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₁) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₂))) (Matrix.submatrix.{u3, u2, u1, u1, u2} n m m n α (Inv.inv.{max u1 u3} (Matrix.{u1, u1, u3} m m α) (Matrix.inv.{u1, u3} m α _inst_4 (fun (a : m) (b : m) => _inst_5 a b) _inst_3) A) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₂) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₁))
+  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] [_inst_4 : Fintype.{u1} m] [_inst_5 : DecidableEq.{succ u1} m] (A : Matrix.{u1, u1, u3} m m α) (e₁ : Equiv.{succ u2, succ u1} n m) (e₂ : Equiv.{succ u2, succ u1} n m), Eq.{max (succ u2) (succ u3)} (Matrix.{u2, u2, u3} n n α) (Inv.inv.{max u3 u2} (Matrix.{u2, u2, u3} n n α) (Matrix.inv.{u2, u3} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) (Matrix.submatrix.{u3, u2, u1, u1, u2} n m m n α A (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₁) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₂))) (Matrix.submatrix.{u3, u2, u1, u1, u2} n m m n α (Inv.inv.{max u1 u3} (Matrix.{u1, u1, u3} m m α) (Matrix.inv.{u1, u3} m α _inst_4 (fun (a : m) (b : m) => _inst_5 a b) _inst_3) A) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₂) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₁))
 Case conversion may be inaccurate. Consider using '#align matrix.inv_submatrix_equiv Matrix.inv_submatrix_equivₓ'. -/
 @[simp]
 theorem inv_submatrix_equiv (A : Matrix m m α) (e₁ e₂ : n ≃ m) :
@@ -1252,7 +1252,7 @@ theorem inv_submatrix_equiv (A : Matrix m m α) (e₁ e₂ : n ≃ m) :
 lean 3 declaration is
   forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] [_inst_4 : Fintype.{u1} m] [_inst_5 : DecidableEq.{succ u1} m] (e₁ : Equiv.{succ u2, succ u1} n m) (e₂ : Equiv.{succ u2, succ u1} n m) (A : Matrix.{u2, u2, u3} n n α), Eq.{succ (max u1 u3)} (Matrix.{u1, u1, u3} m m α) (Inv.inv.{max u1 u3} (Matrix.{u1, u1, u3} m m α) (Matrix.hasInv.{u1, u3} m α _inst_4 (fun (a : m) (b : m) => _inst_5 a b) _inst_3) (coeFn.{max 1 (max (succ (max u2 u3)) (succ (max u1 u3))) (succ (max u1 u3)) (succ (max u2 u3)), max (succ (max u2 u3)) (succ (max u1 u3))} (Equiv.{succ (max u2 u3), succ (max u1 u3)} (Matrix.{u2, u2, u3} n n α) (Matrix.{u1, u1, u3} m m α)) (fun (_x : Equiv.{succ (max u2 u3), succ (max u1 u3)} (Matrix.{u2, u2, u3} n n α) (Matrix.{u1, u1, u3} m m α)) => (Matrix.{u2, u2, u3} n n α) -> (Matrix.{u1, u1, u3} m m α)) (Equiv.hasCoeToFun.{succ (max u2 u3), succ (max u1 u3)} (Matrix.{u2, u2, u3} n n α) (Matrix.{u1, u1, u3} m m α)) (Matrix.reindex.{u3, u1, u2, u2, u1} m n n m α e₁ e₂) A)) (coeFn.{max 1 (max (succ (max u2 u3)) (succ (max u1 u3))) (succ (max u1 u3)) (succ (max u2 u3)), max (succ (max u2 u3)) (succ (max u1 u3))} (Equiv.{succ (max u2 u3), succ (max u1 u3)} (Matrix.{u2, u2, u3} n n α) (Matrix.{u1, u1, u3} m m α)) (fun (_x : Equiv.{succ (max u2 u3), succ (max u1 u3)} (Matrix.{u2, u2, u3} n n α) (Matrix.{u1, u1, u3} m m α)) => (Matrix.{u2, u2, u3} n n α) -> (Matrix.{u1, u1, u3} m m α)) (Equiv.hasCoeToFun.{succ (max u2 u3), succ (max u1 u3)} (Matrix.{u2, u2, u3} n n α) (Matrix.{u1, u1, u3} m m α)) (Matrix.reindex.{u3, u1, u2, u2, u1} m n n m α e₂ e₁) (Inv.inv.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.hasInv.{u2, u3} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A))
 but is expected to have type
-  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] [_inst_4 : Fintype.{u1} m] [_inst_5 : DecidableEq.{succ u1} m] (e₁ : Equiv.{succ u2, succ u1} n m) (e₂ : Equiv.{succ u2, succ u1} n m) (A : Matrix.{u2, u2, u3} n n α), Eq.{max (succ u1) (succ u3)} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Matrix.{u2, u2, u3} n n α) => Matrix.{u1, u1, u3} m m α) A) (Inv.inv.{max u1 u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Matrix.{u2, u2, u3} n n α) => Matrix.{u1, u1, u3} m m α) A) (Matrix.inv.{u1, u3} m α _inst_4 (fun (a : m) (b : m) => _inst_5 a b) _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u2) (succ u3), max (succ u1) (succ u3)} (Equiv.{max (succ u3) (succ u2), max (succ u3) (succ u1)} (Matrix.{u2, u2, u3} n n α) (Matrix.{u1, u1, u3} m m α)) (Matrix.{u2, u2, u3} n n α) (fun (_x : Matrix.{u2, u2, u3} n n α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Matrix.{u2, u2, u3} n n α) => Matrix.{u1, u1, u3} m m α) _x) (Equiv.instFunLikeEquiv.{max (succ u2) (succ u3), max (succ u1) (succ u3)} (Matrix.{u2, u2, u3} n n α) (Matrix.{u1, u1, u3} m m α)) (Matrix.reindex.{u3, u1, u2, u2, u1} m n n m α e₁ e₂) A)) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u2) (succ u3), max (succ u1) (succ u3)} (Equiv.{max (succ u3) (succ u2), max (succ u3) (succ u1)} (Matrix.{u2, u2, u3} n n α) (Matrix.{u1, u1, u3} m m α)) (Matrix.{u2, u2, u3} n n α) (fun (_x : Matrix.{u2, u2, u3} n n α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Matrix.{u2, u2, u3} n n α) => Matrix.{u1, u1, u3} m m α) _x) (Equiv.instFunLikeEquiv.{max (succ u2) (succ u3), max (succ u1) (succ u3)} (Matrix.{u2, u2, u3} n n α) (Matrix.{u1, u1, u3} m m α)) (Matrix.reindex.{u3, u1, u2, u2, u1} m n n m α e₂ e₁) (Inv.inv.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.inv.{u2, u3} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A))
+  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] [_inst_4 : Fintype.{u1} m] [_inst_5 : DecidableEq.{succ u1} m] (e₁ : Equiv.{succ u2, succ u1} n m) (e₂ : Equiv.{succ u2, succ u1} n m) (A : Matrix.{u2, u2, u3} n n α), Eq.{max (succ u1) (succ u3)} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Matrix.{u2, u2, u3} n n α) => Matrix.{u1, u1, u3} m m α) A) (Inv.inv.{max u1 u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Matrix.{u2, u2, u3} n n α) => Matrix.{u1, u1, u3} m m α) A) (Matrix.inv.{u1, u3} m α _inst_4 (fun (a : m) (b : m) => _inst_5 a b) _inst_3) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u2) (succ u3), max (succ u1) (succ u3)} (Equiv.{max (succ u3) (succ u2), max (succ u3) (succ u1)} (Matrix.{u2, u2, u3} n n α) (Matrix.{u1, u1, u3} m m α)) (Matrix.{u2, u2, u3} n n α) (fun (_x : Matrix.{u2, u2, u3} n n α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Matrix.{u2, u2, u3} n n α) => Matrix.{u1, u1, u3} m m α) _x) (Equiv.instFunLikeEquiv.{max (succ u2) (succ u3), max (succ u1) (succ u3)} (Matrix.{u2, u2, u3} n n α) (Matrix.{u1, u1, u3} m m α)) (Matrix.reindex.{u3, u1, u2, u2, u1} m n n m α e₁ e₂) A)) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), max (succ u2) (succ u3), max (succ u1) (succ u3)} (Equiv.{max (succ u3) (succ u2), max (succ u3) (succ u1)} (Matrix.{u2, u2, u3} n n α) (Matrix.{u1, u1, u3} m m α)) (Matrix.{u2, u2, u3} n n α) (fun (_x : Matrix.{u2, u2, u3} n n α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Matrix.{u2, u2, u3} n n α) => Matrix.{u1, u1, u3} m m α) _x) (Equiv.instFunLikeEquiv.{max (succ u2) (succ u3), max (succ u1) (succ u3)} (Matrix.{u2, u2, u3} n n α) (Matrix.{u1, u1, u3} m m α)) (Matrix.reindex.{u3, u1, u2, u2, u1} m n n m α e₂ e₁) (Inv.inv.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.inv.{u2, u3} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A))
 Case conversion may be inaccurate. Consider using '#align matrix.inv_reindex Matrix.inv_reindexₓ'. -/
 theorem inv_reindex (e₁ e₂ : n ≃ m) (A : Matrix n n α) : (reindex e₁ e₂ A)⁻¹ = reindex e₂ e₁ A⁻¹ :=
   inv_submatrix_equiv A e₁.symm e₂.symm

mathlib commit https://github.com/leanprover-community/mathlib/commit/c89fe2d59ae06402c3f55f978016d1ada444f57e

@@ -1118,7 +1118,7 @@ theorem list_prod_inv_reverse : ∀ l : List (Matrix n n α), l.Prod⁻¹ = (l.r
 lean 3 declaration is
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(CommRing.toRing.{u2} α _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Pi.Function.module.{u1, u2, u2} n α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.cramer.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 A) b))
 but is expected to have type
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(fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Matrix.cramer.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 A) b))
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(a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (n -> α) (fun (_x : n -> α) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : n -> α) => n -> α) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, max u1 u2} α α (n -> α) (n -> α) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Matrix.cramer.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 A) b))
 Case conversion may be inaccurate. Consider using '#align matrix.det_smul_inv_mul_vec_eq_cramer Matrix.det_smul_inv_mulVec_eq_cramerₓ'. -/
 /-- One form of **Cramer's rule**. See `matrix.mul_vec_cramer` for a stronger form. -/
 @[simp]
@@ -1132,7 +1132,7 @@ theorem det_smul_inv_mulVec_eq_cramer (A : Matrix n n α) (b : n → α) (h : Is
 lean 3 declaration is
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 but is expected to have type
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(fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Matrix.cramer.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 (Matrix.transpose.{u2, u1, u1} n n α A)) b))
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(NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) _inst_1 b (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u2, u2, max u1 u2, max u1 u2} α α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (n -> α) (n -> α) (Pi.addCommMonoid.{u1, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (n -> α) (fun (_x : n -> α) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : n -> α) => n -> α) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, max u1 u2} α α (n -> α) (n -> α) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Matrix.cramer.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 (Matrix.transpose.{u2, u1, u1} n n α A)) b))
 Case conversion may be inaccurate. Consider using '#align matrix.det_smul_inv_vec_mul_eq_cramer_transpose Matrix.det_smul_inv_vecMul_eq_cramer_transposeₓ'. -/
 /-- One form of **Cramer's rule**. See `matrix.mul_vec_cramer` for a stronger form. -/
 @[simp]

mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8

@@ -1118,7 +1118,7 @@ theorem list_prod_inv_reverse : ∀ l : List (Matrix n n α), l.Prod⁻¹ = (l.r
 lean 3 declaration is
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α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) => (n -> α) -> n -> α) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, max u1 u2} α α (n -> α) (n -> α) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.Function.module.{u1, u2, u2} n α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Pi.Function.module.{u1, u2, u2} n α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.cramer.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 A) b))
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (b : n -> α), (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{max (succ u1) (succ u2)} (n -> α) (HSMul.hSMul.{u2, max u1 u2, max u1 u2} α (n -> α) (n -> α) (instHSMul.{u2, max u1 u2} α (n -> α) (Pi.instSMul.{u1, u2, u2} n α (fun (a._@.Mathlib.Data.Matrix.Basic._hyg.18074 : n) => α) (fun (i : n) => Algebra.toSMul.{u2, u2} α α (CommRing.toCommSemiring.{u2} α _inst_3) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (Algebra.id.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) (Matrix.mulVec.{u2, u1, u1} n n α 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(a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (n -> α) (fun (_x : n -> α) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : n -> α) => n -> α) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, max u1 u2} α α (n -> α) (n -> α) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Matrix.cramer.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 A) b))
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (b : n -> α), (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{max (succ u1) (succ u2)} (n -> α) (HSMul.hSMul.{u2, max u1 u2, max u1 u2} α (n -> α) (n -> α) (instHSMul.{u2, max u1 u2} α (n -> α) (Pi.instSMul.{u1, u2, u2} n α (fun (a._@.Mathlib.Data.Matrix.Basic._hyg.18074 : n) => α) (fun (i : n) => Algebra.toSMul.{u2, u2} α α (CommRing.toCommSemiring.{u2} α _inst_3) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (Algebra.id.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) (Matrix.mulVec.{u2, u1, u1} n n α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) _inst_1 (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) b)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u2, u2, max u1 u2, max u1 u2} α α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (n -> α) (n -> α) (Pi.addCommMonoid.{u1, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (n -> α) (fun (_x : n -> α) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : n -> α) => n -> α) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, max u1 u2} α α (n -> α) (n -> α) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Matrix.cramer.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 A) b))
 Case conversion may be inaccurate. Consider using '#align matrix.det_smul_inv_mul_vec_eq_cramer Matrix.det_smul_inv_mulVec_eq_cramerₓ'. -/
 /-- One form of **Cramer's rule**. See `matrix.mul_vec_cramer` for a stronger form. -/
 @[simp]
@@ -1132,7 +1132,7 @@ theorem det_smul_inv_mulVec_eq_cramer (A : Matrix n n α) (b : n → α) (h : Is
 lean 3 declaration is
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(CommRing.toRing.{u2} α _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Pi.Function.module.{u1, u2, u2} n α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.cramer.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 (Matrix.transpose.{u2, u1, u1} n n α A)) b))
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (b : n -> α), (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{max (succ u1) (succ u2)} (n -> α) (HSMul.hSMul.{u2, max u1 u2, max u1 u2} α (n -> α) (n -> α) (instHSMul.{u2, max u1 u2} α (n -> α) (Pi.instSMul.{u1, u2, u2} n α (fun (a._@.Mathlib.Data.Matrix.Basic._hyg.18132 : n) => α) (fun (i : n) => Algebra.toSMul.{u2, u2} α α (CommRing.toCommSemiring.{u2} α _inst_3) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (Algebra.id.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) (Matrix.vecMul.{u2, u1, u1} n n α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) _inst_1 b (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u2, u2, max u1 u2, max u1 u2} α α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (n -> α) (n -> α) (Pi.addCommMonoid.{u1, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (n -> α) (fun (_x : n -> α) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : n -> α) => n -> α) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, max u1 u2} α α (n -> α) (n -> α) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Matrix.cramer.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 (Matrix.transpose.{u2, u1, u1} n n α A)) b))
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (b : n -> α), (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{max (succ u1) (succ u2)} (n -> α) (HSMul.hSMul.{u2, max u1 u2, max u1 u2} α (n -> α) (n -> α) (instHSMul.{u2, max u1 u2} α (n -> α) (Pi.instSMul.{u1, u2, u2} n α (fun (a._@.Mathlib.Data.Matrix.Basic._hyg.18132 : n) => α) (fun (i : n) => Algebra.toSMul.{u2, u2} α α (CommRing.toCommSemiring.{u2} α _inst_3) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (Algebra.id.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) (Matrix.vecMul.{u2, u1, u1} n n α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) _inst_1 b (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u2, u2, max u1 u2, max u1 u2} α α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (n -> α) (n -> α) (Pi.addCommMonoid.{u1, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (n -> α) (fun (_x : n -> α) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : n -> α) => n -> α) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, max u1 u2} α α (n -> α) (n -> α) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.273 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Matrix.cramer.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 (Matrix.transpose.{u2, u1, u1} n n α A)) b))
 Case conversion may be inaccurate. Consider using '#align matrix.det_smul_inv_vec_mul_eq_cramer_transpose Matrix.det_smul_inv_vecMul_eq_cramer_transposeₓ'. -/
 /-- One form of **Cramer's rule**. See `matrix.mul_vec_cramer` for a stronger form. -/
 @[simp]

mathlib commit https://github.com/leanprover-community/mathlib/commit/08e1d8d4d989df3a6df86f385e9053ec8a372cc1

@@ -76,7 +76,7 @@ variable [Fintype n] [DecidableEq n] [CommRing α]
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) A], Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Invertible.invOf.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) A _inst_4) A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.one.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))))))
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) A], Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Invertible.invOf.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) A _inst_4) A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))))
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) A], Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Invertible.invOf.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) A _inst_4) A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))))
 Case conversion may be inaccurate. Consider using '#align matrix.inv_of_mul_self Matrix.invOf_mul_selfₓ'. -/
 /-- A copy of `inv_of_mul_self` using `⬝` not `*`. -/
 protected theorem invOf_mul_self (A : Matrix n n α) [Invertible A] : ⅟ A ⬝ A = 1 :=
@@ -87,7 +87,7 @@ protected theorem invOf_mul_self (A : Matrix n n α) [Invertible A] : ⅟ A ⬝
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) A], Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A (Invertible.invOf.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) A _inst_4)) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.one.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))))))
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) A], Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A (Invertible.invOf.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) A _inst_4)) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))))
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) A], Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A (Invertible.invOf.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) A _inst_4)) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))))
 Case conversion may be inaccurate. Consider using '#align matrix.mul_inv_of_self Matrix.mul_invOf_selfₓ'. -/
 /-- A copy of `mul_inv_of_self` using `⬝` not `*`. -/
 protected theorem mul_invOf_self (A : Matrix n n α) [Invertible A] : A ⬝ ⅟ A = 1 :=
@@ -98,7 +98,7 @@ protected theorem mul_invOf_self (A : Matrix n n α) [Invertible A] : A ⬝ ⅟
 lean 3 declaration is
   forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] (A : Matrix.{u2, u2, u3} n n α) (B : Matrix.{u2, u1, u3} n m α) [_inst_4 : Invertible.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.hasMul.{u3, u2} n α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.hasOne.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u3} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (AddMonoidWithOne.toOne.{u3} α (AddGroupWithOne.toAddMonoidWithOne.{u3} α (AddCommGroupWithOne.toAddGroupWithOne.{u3} α (Ring.toAddCommGroupWithOne.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) A], Eq.{succ (max u2 u1 u3)} (Matrix.{u2, u1, u3} n m α) (Matrix.mul.{u3, u2, u2, u1} n n m α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) (Invertible.invOf.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.hasMul.{u3, u2} n α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.hasOne.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u3} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (AddMonoidWithOne.toOne.{u3} α (AddGroupWithOne.toAddMonoidWithOne.{u3} α (AddCommGroupWithOne.toAddGroupWithOne.{u3} α (Ring.toAddCommGroupWithOne.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) A _inst_4) (Matrix.mul.{u3, u2, u2, u1} n n m α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) A B)) B
 but is expected to have type
-  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] (A : Matrix.{u2, u2, u3} n n α) (B : Matrix.{u2, u1, u3} n m α) [_inst_4 : Invertible.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.instMulMatrix.{u3, u2} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (NonAssocRing.toOne.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) A], Eq.{max (max (succ u1) (succ u2)) (succ u3)} (Matrix.{u2, u1, u3} n m α) (Matrix.mul.{u3, u2, u2, u1} n n m α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) (Invertible.invOf.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.instMulMatrix.{u3, u2} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (NonAssocRing.toOne.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) A _inst_4) (Matrix.mul.{u3, u2, u2, u1} n n m α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) A B)) B
+  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] (A : Matrix.{u2, u2, u3} n n α) (B : Matrix.{u2, u1, u3} n m α) [_inst_4 : Invertible.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.instMulMatrix.{u3, u2} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (Semiring.toOne.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) A], Eq.{max (max (succ u1) (succ u2)) (succ u3)} (Matrix.{u2, u1, u3} n m α) (Matrix.mul.{u3, u2, u2, u1} n n m α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) (Invertible.invOf.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.instMulMatrix.{u3, u2} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (Semiring.toOne.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) A _inst_4) (Matrix.mul.{u3, u2, u2, u1} n n m α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) A B)) B
 Case conversion may be inaccurate. Consider using '#align matrix.inv_of_mul_self_assoc Matrix.invOf_mul_self_assocₓ'. -/
 /-- A copy of `inv_of_mul_self_assoc` using `⬝` not `*`. -/
 protected theorem invOf_mul_self_assoc (A : Matrix n n α) (B : Matrix n m α) [Invertible A] :
@@ -109,7 +109,7 @@ protected theorem invOf_mul_self_assoc (A : Matrix n n α) (B : Matrix n m α) [
 lean 3 declaration is
   forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] (A : Matrix.{u2, u2, u3} n n α) (B : Matrix.{u2, u1, u3} n m α) [_inst_4 : Invertible.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.hasMul.{u3, u2} n α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.hasOne.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u3} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (AddMonoidWithOne.toOne.{u3} α (AddGroupWithOne.toAddMonoidWithOne.{u3} α (AddCommGroupWithOne.toAddGroupWithOne.{u3} α (Ring.toAddCommGroupWithOne.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) A], Eq.{succ (max u2 u1 u3)} (Matrix.{u2, u1, u3} n m α) (Matrix.mul.{u3, u2, u2, u1} n n m α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) A (Matrix.mul.{u3, u2, u2, u1} n n m α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) (Invertible.invOf.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.hasMul.{u3, u2} n α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.hasOne.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u3} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (AddMonoidWithOne.toOne.{u3} α (AddGroupWithOne.toAddMonoidWithOne.{u3} α (AddCommGroupWithOne.toAddGroupWithOne.{u3} α (Ring.toAddCommGroupWithOne.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) A _inst_4) B)) B
 but is expected to have type
-  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] (A : Matrix.{u2, u2, u3} n n α) (B : Matrix.{u2, u1, u3} n m α) [_inst_4 : Invertible.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.instMulMatrix.{u3, u2} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (NonAssocRing.toOne.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) A], Eq.{max (max (succ u1) (succ u2)) (succ u3)} (Matrix.{u2, u1, u3} n m α) (Matrix.mul.{u3, u2, u2, u1} n n m α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) A (Matrix.mul.{u3, u2, u2, u1} n n m α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) (Invertible.invOf.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.instMulMatrix.{u3, u2} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (NonAssocRing.toOne.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) A _inst_4) B)) B
+  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] (A : Matrix.{u2, u2, u3} n n α) (B : Matrix.{u2, u1, u3} n m α) [_inst_4 : Invertible.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.instMulMatrix.{u3, u2} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (Semiring.toOne.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) A], Eq.{max (max (succ u1) (succ u2)) (succ u3)} (Matrix.{u2, u1, u3} n m α) (Matrix.mul.{u3, u2, u2, u1} n n m α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) A (Matrix.mul.{u3, u2, u2, u1} n n m α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) (Invertible.invOf.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.instMulMatrix.{u3, u2} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (Semiring.toOne.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) A _inst_4) B)) B
 Case conversion may be inaccurate. Consider using '#align matrix.mul_inv_of_self_assoc Matrix.mul_invOf_self_assocₓ'. -/
 /-- A copy of `mul_inv_of_self_assoc` using `⬝` not `*`. -/
 protected theorem mul_invOf_self_assoc (A : Matrix n n α) (B : Matrix n m α) [Invertible A] :
@@ -120,7 +120,7 @@ protected theorem mul_invOf_self_assoc (A : Matrix n n α) (B : Matrix n m α) [
 lean 3 declaration is
   forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] (A : Matrix.{u1, u2, u3} m n α) (B : Matrix.{u2, u2, u3} n n α) [_inst_4 : Invertible.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.hasMul.{u3, u2} n α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.hasOne.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u3} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (AddMonoidWithOne.toOne.{u3} α (AddGroupWithOne.toAddMonoidWithOne.{u3} α (AddCommGroupWithOne.toAddGroupWithOne.{u3} α (Ring.toAddCommGroupWithOne.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) B], Eq.{succ (max u1 u2 u3)} (Matrix.{u1, u2, u3} m n α) (Matrix.mul.{u3, u1, u2, u2} m n n α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) (Matrix.mul.{u3, u1, u2, u2} m n n α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) A (Invertible.invOf.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.hasMul.{u3, u2} n α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.hasOne.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u3} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (AddMonoidWithOne.toOne.{u3} α (AddGroupWithOne.toAddMonoidWithOne.{u3} α (AddCommGroupWithOne.toAddGroupWithOne.{u3} α (Ring.toAddCommGroupWithOne.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) B _inst_4)) B) A
 but is expected to have type
-  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] (A : Matrix.{u1, u2, u3} m n α) (B : Matrix.{u2, u2, u3} n n α) [_inst_4 : Invertible.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.instMulMatrix.{u3, u2} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (NonAssocRing.toOne.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) B], Eq.{max (max (succ u1) (succ u2)) (succ u3)} (Matrix.{u1, u2, u3} m n α) (Matrix.mul.{u3, u1, u2, u2} m n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) (Matrix.mul.{u3, u1, u2, u2} m n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) A (Invertible.invOf.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.instMulMatrix.{u3, u2} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (NonAssocRing.toOne.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) B _inst_4)) B) A
+  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] (A : Matrix.{u1, u2, u3} m n α) (B : Matrix.{u2, u2, u3} n n α) [_inst_4 : Invertible.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.instMulMatrix.{u3, u2} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (Semiring.toOne.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) B], Eq.{max (max (succ u1) (succ u2)) (succ u3)} (Matrix.{u1, u2, u3} m n α) (Matrix.mul.{u3, u1, u2, u2} m n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) (Matrix.mul.{u3, u1, u2, u2} m n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) A (Invertible.invOf.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.instMulMatrix.{u3, u2} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (Semiring.toOne.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) B _inst_4)) B) A
 Case conversion may be inaccurate. Consider using '#align matrix.mul_inv_of_mul_self_cancel Matrix.mul_invOf_mul_self_cancelₓ'. -/
 /-- A copy of `mul_inv_of_mul_self_cancel` using `⬝` not `*`. -/
 protected theorem mul_invOf_mul_self_cancel (A : Matrix m n α) (B : Matrix n n α) [Invertible B] :
@@ -131,7 +131,7 @@ protected theorem mul_invOf_mul_self_cancel (A : Matrix m n α) (B : Matrix n n
 lean 3 declaration is
   forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] (A : Matrix.{u1, u2, u3} m n α) (B : Matrix.{u2, u2, u3} n n α) [_inst_4 : Invertible.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.hasMul.{u3, u2} n α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.hasOne.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u3} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (AddMonoidWithOne.toOne.{u3} α (AddGroupWithOne.toAddMonoidWithOne.{u3} α (AddCommGroupWithOne.toAddGroupWithOne.{u3} α (Ring.toAddCommGroupWithOne.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) B], Eq.{succ (max u1 u2 u3)} (Matrix.{u1, u2, u3} m n α) (Matrix.mul.{u3, u1, u2, u2} m n n α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) (Matrix.mul.{u3, u1, u2, u2} m n n α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) A B) (Invertible.invOf.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.hasMul.{u3, u2} n α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.hasOne.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u3} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (AddMonoidWithOne.toOne.{u3} α (AddGroupWithOne.toAddMonoidWithOne.{u3} α (AddCommGroupWithOne.toAddGroupWithOne.{u3} α (Ring.toAddCommGroupWithOne.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) B _inst_4)) A
 but is expected to have type
-  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] (A : Matrix.{u1, u2, u3} m n α) (B : Matrix.{u2, u2, u3} n n α) [_inst_4 : Invertible.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.instMulMatrix.{u3, u2} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (NonAssocRing.toOne.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) B], Eq.{max (max (succ u1) (succ u2)) (succ u3)} (Matrix.{u1, u2, u3} m n α) (Matrix.mul.{u3, u1, u2, u2} m n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) (Matrix.mul.{u3, u1, u2, u2} m n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) A B) (Invertible.invOf.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.instMulMatrix.{u3, u2} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (NonAssocRing.toOne.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) B _inst_4)) A
+  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] (A : Matrix.{u1, u2, u3} m n α) (B : Matrix.{u2, u2, u3} n n α) [_inst_4 : Invertible.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.instMulMatrix.{u3, u2} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (Semiring.toOne.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) B], Eq.{max (max (succ u1) (succ u2)) (succ u3)} (Matrix.{u1, u2, u3} m n α) (Matrix.mul.{u3, u1, u2, u2} m n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) (Matrix.mul.{u3, u1, u2, u2} m n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) A B) (Invertible.invOf.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.instMulMatrix.{u3, u2} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (Semiring.toOne.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) B _inst_4)) A
 Case conversion may be inaccurate. Consider using '#align matrix.mul_mul_inv_of_self_cancel Matrix.mul_mul_invOf_self_cancelₓ'. -/
 /-- A copy of `mul_mul_inv_of_self_cancel` using `⬝` not `*`. -/
 protected theorem mul_mul_invOf_self_cancel (A : Matrix m n α) (B : Matrix n n α) [Invertible B] :
@@ -144,7 +144,7 @@ variable (A : Matrix n n α) (B : Matrix n n α)
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)], Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) A
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{u2} α (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)], Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) A
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{u2} α (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)], Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) A
 Case conversion may be inaccurate. Consider using '#align matrix.invertible_of_det_invertible Matrix.invertibleOfDetInvertibleₓ'. -/
 /-- If `A.det` has a constructive inverse, produce one for `A`. -/
 def invertibleOfDetInvertible [Invertible A.det] : Invertible A
@@ -160,7 +160,7 @@ def invertibleOfDetInvertible [Invertible A.det] : Invertible A
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)] [_inst_5 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) A], Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Invertible.invOf.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) A _inst_5) (SMul.smul.{u2, max u1 u2} α (Matrix.{u1, u1, u2} n n α) (Matrix.hasSmul.{u2, u1, u1, u2} n n α α (Mul.toSMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Invertible.invOf.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) _inst_4) (Matrix.adjugate.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 A))
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{u2} α (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)] [_inst_5 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) A], Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Invertible.invOf.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) A _inst_5) (HSMul.hSMul.{u2, max u1 u2, max u1 u2} α (Matrix.{u1, u1, u2} n n α) (Matrix.{u1, u1, u2} n n α) (instHSMul.{u2, max u1 u2} α (Matrix.{u1, u1, u2} n n α) (Matrix.smul.{u2, u1, u1, u2} n n α α (Algebra.toSMul.{u2, u2} α α (CommRing.toCommSemiring.{u2} α _inst_3) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Algebra.id.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Invertible.invOf.{u2} α (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) _inst_4) (Matrix.adjugate.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 A))
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{u2} α (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)] [_inst_5 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) A], Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Invertible.invOf.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) A _inst_5) (HSMul.hSMul.{u2, max u1 u2, max u1 u2} α (Matrix.{u1, u1, u2} n n α) (Matrix.{u1, u1, u2} n n α) (instHSMul.{u2, max u1 u2} α (Matrix.{u1, u1, u2} n n α) (Matrix.smul.{u2, u1, u1, u2} n n α α (Algebra.toSMul.{u2, u2} α α (CommRing.toCommSemiring.{u2} α _inst_3) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (Algebra.id.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Invertible.invOf.{u2} α (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) _inst_4) (Matrix.adjugate.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 A))
 Case conversion may be inaccurate. Consider using '#align matrix.inv_of_eq Matrix.invOf_eqₓ'. -/
 theorem invOf_eq [Invertible A.det] [Invertible A] : ⅟ A = ⅟ A.det • A.adjugate :=
   by
@@ -172,7 +172,7 @@ theorem invOf_eq [Invertible A.det] [Invertible A] : ⅟ A = ⅟ A.det • A.adj
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (B : Matrix.{u1, u1, u2} n n α), (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) B A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.one.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))))))) -> (Invertible.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A))
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (B : Matrix.{u1, u1, u2} n n α), (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) B A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))))) -> (Invertible.{u2} α (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A))
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (B : Matrix.{u1, u1, u2} n n α), (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) B A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))))) -> (Invertible.{u2} α (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A))
 Case conversion may be inaccurate. Consider using '#align matrix.det_invertible_of_left_inverse Matrix.detInvertibleOfLeftInverseₓ'. -/
 /-- `A.det` is invertible if `A` has a left inverse. -/
 def detInvertibleOfLeftInverse (h : B ⬝ A = 1) : Invertible A.det
@@ -186,7 +186,7 @@ def detInvertibleOfLeftInverse (h : B ⬝ A = 1) : Invertible A.det
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (B : Matrix.{u1, u1, u2} n n α), (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A B) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.one.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))))))) -> (Invertible.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A))
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (B : Matrix.{u1, u1, u2} n n α), (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A B) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))))) -> (Invertible.{u2} α (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A))
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (B : Matrix.{u1, u1, u2} n n α), (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A B) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))))) -> (Invertible.{u2} α (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A))
 Case conversion may be inaccurate. Consider using '#align matrix.det_invertible_of_right_inverse Matrix.detInvertibleOfRightInverseₓ'. -/
 /-- `A.det` is invertible if `A` has a right inverse. -/
 def detInvertibleOfRightInverse (h : A ⬝ B = 1) : Invertible A.det
@@ -200,7 +200,7 @@ def detInvertibleOfRightInverse (h : A ⬝ B = 1) : Invertible A.det
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) A], Invertible.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) A], Invertible.{u2} α (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) A], Invertible.{u2} α (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)
 Case conversion may be inaccurate. Consider using '#align matrix.det_invertible_of_invertible Matrix.detInvertibleOfInvertibleₓ'. -/
 /-- If `A` has a constructive inverse, produce one for `A.det`. -/
 def detInvertibleOfInvertible [Invertible A] : Invertible A.det :=
@@ -211,7 +211,7 @@ def detInvertibleOfInvertible [Invertible A] : Invertible A.det :=
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) A] [_inst_5 : Invertible.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)], Eq.{succ u2} α (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 (Invertible.invOf.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) A _inst_4)) (Invertible.invOf.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) _inst_5)
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) A] [_inst_5 : Invertible.{u2} α (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)], Eq.{succ u2} α (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 (Invertible.invOf.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) A _inst_4)) (Invertible.invOf.{u2} α (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) _inst_5)
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) A] [_inst_5 : Invertible.{u2} α (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)], Eq.{succ u2} α (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 (Invertible.invOf.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) A _inst_4)) (Invertible.invOf.{u2} α (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) _inst_5)
 Case conversion may be inaccurate. Consider using '#align matrix.det_inv_of Matrix.det_invOfₓ'. -/
 theorem det_invOf [Invertible A] [Invertible A.det] : (⅟ A).det = ⅟ A.det :=
   by
@@ -223,7 +223,7 @@ theorem det_invOf [Invertible A] [Invertible A.det] : (⅟ A).det = ⅟ A.det :=
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), Equiv.{succ (max u1 u2), succ u2} (Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) A) (Invertible.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A))
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), Equiv.{succ (max u1 u2), succ u2} (Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) A) (Invertible.{u2} α (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A))
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), Equiv.{succ (max u1 u2), succ u2} (Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) A) (Invertible.{u2} α (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A))
 Case conversion may be inaccurate. Consider using '#align matrix.invertible_equiv_det_invertible Matrix.invertibleEquivDetInvertibleₓ'. -/
 /-- Together `matrix.det_invertible_of_invertible` and `matrix.invertible_of_det_invertible` form an
 equivalence, although both sides of the equiv are subsingleton anyway. -/
@@ -242,7 +242,7 @@ variable {A B}
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {A : Matrix.{u1, u1, u2} n n α} {B : Matrix.{u1, u1, u2} n n α}, Iff (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A B) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.one.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))))))) (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) B A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.one.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3))))))))))
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {A : Matrix.{u1, u1, u2} n n α} {B : Matrix.{u1, u1, u2} n n α}, Iff (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A B) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))))) (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) B A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))))
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {A : Matrix.{u1, u1, u2} n n α} {B : Matrix.{u1, u1, u2} n n α}, Iff (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A B) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))))) (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) B A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))))
 Case conversion may be inaccurate. Consider using '#align matrix.mul_eq_one_comm Matrix.mul_eq_one_commₓ'. -/
 theorem mul_eq_one_comm : A ⬝ B = 1 ↔ B ⬝ A = 1 :=
   suffices ∀ A B, A ⬝ B = 1 → B ⬝ A = 1 from ⟨this A B, this B A⟩
@@ -263,7 +263,7 @@ variable (A B)
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (B : Matrix.{u1, u1, u2} n n α), (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) B A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.one.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))))))) -> (Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) A)
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (B : Matrix.{u1, u1, u2} n n α), (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) B A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))))) -> (Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) A)
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (B : Matrix.{u1, u1, u2} n n α), (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) B A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))))) -> (Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) A)
 Case conversion may be inaccurate. Consider using '#align matrix.invertible_of_left_inverse Matrix.invertibleOfLeftInverseₓ'. -/
 /-- We can construct an instance of invertible A if A has a left inverse. -/
 def invertibleOfLeftInverse (h : B ⬝ A = 1) : Invertible A :=
@@ -274,7 +274,7 @@ def invertibleOfLeftInverse (h : B ⬝ A = 1) : Invertible A :=
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (B : Matrix.{u1, u1, u2} n n α), (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A B) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.one.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))))))) -> (Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) A)
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (B : Matrix.{u1, u1, u2} n n α), (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A B) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))))) -> (Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) A)
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (B : Matrix.{u1, u1, u2} n n α), (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A B) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))))) -> (Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) A)
 Case conversion may be inaccurate. Consider using '#align matrix.invertible_of_right_inverse Matrix.invertibleOfRightInverseₓ'. -/
 /-- We can construct an instance of invertible A if A has a right inverse. -/
 def invertibleOfRightInverse (h : A ⬝ B = 1) : Invertible A :=
@@ -285,7 +285,7 @@ def invertibleOfRightInverse (h : A ⬝ B = 1) : Invertible A :=
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) A], Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.transpose.{u2, u1, u1} n n α A)
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) A], Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.transpose.{u2, u1, u1} n n α A)
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) A], Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Matrix.transpose.{u2, u1, u1} n n α A)
 Case conversion may be inaccurate. Consider using '#align matrix.invertible_transpose Matrix.invertibleTransposeₓ'. -/
 /-- The transpose of an invertible matrix is invertible. -/
 instance invertibleTranspose [Invertible A] : Invertible Aᵀ :=
@@ -297,7 +297,7 @@ instance invertibleTranspose [Invertible A] : Invertible Aᵀ :=
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.transpose.{u2, u1, u1} n n α A)], Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) A
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.transpose.{u2, u1, u1} n n α A)], Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) A
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Matrix.transpose.{u2, u1, u1} n n α A)], Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) A
 Case conversion may be inaccurate. Consider using '#align matrix.invertible__of_invertible_transpose Matrix.invertibleOfInvertibleTransposeₓ'. -/
 /-- A matrix is invertible if the transpose is invertible. -/
 def invertibleOfInvertibleTranspose [Invertible Aᵀ] : Invertible A :=
@@ -310,7 +310,7 @@ def invertibleOfInvertibleTranspose [Invertible Aᵀ] : Invertible A :=
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : StarRing.{u2} α (NonUnitalRing.toNonUnitalSemiring.{u2} α (NonUnitalCommRing.toNonUnitalRing.{u2} α (CommRing.toNonUnitalCommRing.{u2} α _inst_3)))] [_inst_5 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.conjTranspose.{u2, u1, u1} n n α (InvolutiveStar.toHasStar.{u2} α (StarAddMonoid.toHasInvolutiveStar.{u2} α (AddCommMonoid.toAddMonoid.{u2} α (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} α (NonUnitalRing.toNonUnitalSemiring.{u2} α (NonUnitalCommRing.toNonUnitalRing.{u2} α (CommRing.toNonUnitalCommRing.{u2} α _inst_3)))))) (StarRing.toStarAddMonoid.{u2} α (NonUnitalRing.toNonUnitalSemiring.{u2} α (NonUnitalCommRing.toNonUnitalRing.{u2} α (CommRing.toNonUnitalCommRing.{u2} α _inst_3))) _inst_4))) A)], Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) A
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : StarRing.{u2} α (NonUnitalRing.toNonUnitalSemiring.{u2} α (NonUnitalCommRing.toNonUnitalRing.{u2} α (CommRing.toNonUnitalCommRing.{u2} α _inst_3)))] [_inst_5 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.conjTranspose.{u2, u1, u1} n n α (InvolutiveStar.toStar.{u2} α (StarAddMonoid.toInvolutiveStar.{u2} α (AddMonoidWithOne.toAddMonoid.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (Ring.toAddGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (StarRing.toStarAddMonoid.{u2} α (NonUnitalRing.toNonUnitalSemiring.{u2} α (NonUnitalCommRing.toNonUnitalRing.{u2} α (CommRing.toNonUnitalCommRing.{u2} α _inst_3))) _inst_4))) A)], Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) A
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : StarRing.{u2} α (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} α (NonUnitalCommRing.toNonUnitalCommSemiring.{u2} α (CommRing.toNonUnitalCommRing.{u2} α _inst_3)))] [_inst_5 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Matrix.conjTranspose.{u2, u1, u1} n n α (InvolutiveStar.toStar.{u2} α (StarAddMonoid.toInvolutiveStar.{u2} α (AddMonoidWithOne.toAddMonoid.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (Ring.toAddGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (StarRing.toStarAddMonoid.{u2} α (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} α (NonUnitalCommRing.toNonUnitalCommSemiring.{u2} α (CommRing.toNonUnitalCommRing.{u2} α _inst_3))) _inst_4))) A)], Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) A
 Case conversion may be inaccurate. Consider using '#align matrix.invertible_of_invertible_conj_transpose Matrix.invertibleOfInvertibleConjTransposeₓ'. -/
 /-- A matrix is invertible if the conjugate transpose is invertible. -/
 def invertibleOfInvertibleConjTranspose [StarRing α] [Invertible Aᴴ] : Invertible A :=
@@ -323,7 +323,7 @@ def invertibleOfInvertibleConjTranspose [StarRing α] [Invertible Aᴴ] : Invert
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)], Units.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toRing.{u2} α _inst_3)))
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{u2} α (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)], Units.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) _inst_1 (fun (a : n) (b : n) => _inst_2 a b))))
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{u2} α (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)], Units.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_1 (fun (a : n) (b : n) => _inst_2 a b))))
 Case conversion may be inaccurate. Consider using '#align matrix.unit_of_det_invertible Matrix.unitOfDetInvertibleₓ'. -/
 /-- Given a proof that `A.det` has a constructive inverse, lift `A` to `(matrix n n α)ˣ`-/
 def unitOfDetInvertible [Invertible A.det] : (Matrix n n α)ˣ :=
@@ -334,7 +334,7 @@ def unitOfDetInvertible [Invertible A.det] : (Matrix n n α)ˣ :=
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), Iff (IsUnit.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toRing.{u2} α _inst_3))) A) (IsUnit.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A))
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), Iff (IsUnit.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) _inst_1 (fun (a : n) (b : n) => _inst_2 a b)))) A) (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A))
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), Iff (IsUnit.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_1 (fun (a : n) (b : n) => _inst_2 a b)))) A) (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A))
 Case conversion may be inaccurate. Consider using '#align matrix.is_unit_iff_is_unit_det Matrix.isUnit_iff_isUnit_detₓ'. -/
 /-- When lowered to a prop, `matrix.invertible_equiv_det_invertible` forms an `iff`. -/
 theorem isUnit_iff_isUnit_det : IsUnit A ↔ IsUnit A.det := by
@@ -348,7 +348,7 @@ theorem isUnit_iff_isUnit_det : IsUnit A ↔ IsUnit A.det := by
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) A], IsUnit.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) A], IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) A], IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)
 Case conversion may be inaccurate. Consider using '#align matrix.is_unit_det_of_invertible Matrix.isUnit_det_of_invertibleₓ'. -/
 theorem isUnit_det_of_invertible [Invertible A] : IsUnit A.det :=
   @isUnit_of_invertible _ _ _ (detInvertibleOfInvertible A)
@@ -360,7 +360,7 @@ variable {A B}
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {A : Matrix.{u1, u1, u2} n n α} {B : Matrix.{u1, u1, u2} n n α}, (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) B A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.one.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))))))) -> (IsUnit.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toRing.{u2} α _inst_3))) A)
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {A : Matrix.{u1, u1, u2} n n α} {B : Matrix.{u1, u1, u2} n n α}, (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) B A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))))) -> (IsUnit.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) _inst_1 (fun (a : n) (b : n) => _inst_2 a b)))) A)
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {A : Matrix.{u1, u1, u2} n n α} {B : Matrix.{u1, u1, u2} n n α}, (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) B A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))))) -> (IsUnit.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_1 (fun (a : n) (b : n) => _inst_2 a b)))) A)
 Case conversion may be inaccurate. Consider using '#align matrix.is_unit_of_left_inverse Matrix.isUnit_of_left_inverseₓ'. -/
 theorem isUnit_of_left_inverse (h : B ⬝ A = 1) : IsUnit A :=
   ⟨⟨A, B, mul_eq_one_comm.mp h, h⟩, rfl⟩
@@ -370,7 +370,7 @@ theorem isUnit_of_left_inverse (h : B ⬝ A = 1) : IsUnit A :=
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {A : Matrix.{u1, u1, u2} n n α} {B : Matrix.{u1, u1, u2} n n α}, (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A B) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.one.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))))))) -> (IsUnit.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toRing.{u2} α _inst_3))) A)
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {A : Matrix.{u1, u1, u2} n n α} {B : Matrix.{u1, u1, u2} n n α}, (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A B) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))))) -> (IsUnit.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) _inst_1 (fun (a : n) (b : n) => _inst_2 a b)))) A)
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {A : Matrix.{u1, u1, u2} n n α} {B : Matrix.{u1, u1, u2} n n α}, (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A B) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))))) -> (IsUnit.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_1 (fun (a : n) (b : n) => _inst_2 a b)))) A)
 Case conversion may be inaccurate. Consider using '#align matrix.is_unit_of_right_inverse Matrix.isUnit_of_right_inverseₓ'. -/
 theorem isUnit_of_right_inverse (h : A ⬝ B = 1) : IsUnit A :=
   ⟨⟨A, B, h, mul_eq_one_comm.mp h⟩, rfl⟩
@@ -380,7 +380,7 @@ theorem isUnit_of_right_inverse (h : A ⬝ B = 1) : IsUnit A :=
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {A : Matrix.{u1, u1, u2} n n α} {B : Matrix.{u1, u1, u2} n n α}, (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) B A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.one.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))))))) -> (IsUnit.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A))
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {A : Matrix.{u1, u1, u2} n n α} {B : Matrix.{u1, u1, u2} n n α}, (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) B A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))))) -> (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A))
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {A : Matrix.{u1, u1, u2} n n α} {B : Matrix.{u1, u1, u2} n n α}, (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) B A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))))) -> (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A))
 Case conversion may be inaccurate. Consider using '#align matrix.is_unit_det_of_left_inverse Matrix.isUnit_det_of_left_inverseₓ'. -/
 theorem isUnit_det_of_left_inverse (h : B ⬝ A = 1) : IsUnit A.det :=
   @isUnit_of_invertible _ _ _ (detInvertibleOfLeftInverse _ _ h)
@@ -390,7 +390,7 @@ theorem isUnit_det_of_left_inverse (h : B ⬝ A = 1) : IsUnit A.det :=
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {A : Matrix.{u1, u1, u2} n n α} {B : Matrix.{u1, u1, u2} n n α}, (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A B) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.one.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))))))) -> (IsUnit.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A))
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {A : Matrix.{u1, u1, u2} n n α} {B : Matrix.{u1, u1, u2} n n α}, (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A B) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))))) -> (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A))
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {A : Matrix.{u1, u1, u2} n n α} {B : Matrix.{u1, u1, u2} n n α}, (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A B) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))))) -> (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A))
 Case conversion may be inaccurate. Consider using '#align matrix.is_unit_det_of_right_inverse Matrix.isUnit_det_of_right_inverseₓ'. -/
 theorem isUnit_det_of_right_inverse (h : A ⬝ B = 1) : IsUnit A.det :=
   @isUnit_of_invertible _ _ _ (detInvertibleOfRightInverse _ _ h)
@@ -400,7 +400,7 @@ theorem isUnit_det_of_right_inverse (h : A ⬝ B = 1) : IsUnit A.det :=
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {A : Matrix.{u1, u1, u2} n n α} {B : Matrix.{u1, u1, u2} n n α} [_inst_4 : Nontrivial.{u2} α], (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) B A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.one.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))))))) -> (Ne.{succ u2} α (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) (OfNat.ofNat.{u2} α 0 (OfNat.mk.{u2} α 0 (Zero.zero.{u2} α (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))))))))
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {A : Matrix.{u1, u1, u2} n n α} {B : Matrix.{u1, u1, u2} n n α} [_inst_4 : Nontrivial.{u2} α], (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) B A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))))) -> (Ne.{succ u2} α (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) (OfNat.ofNat.{u2} α 0 (Zero.toOfNat0.{u2} α (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))))
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {A : Matrix.{u1, u1, u2} n n α} {B : Matrix.{u1, u1, u2} n n α} [_inst_4 : Nontrivial.{u2} α], (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) B A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))))) -> (Ne.{succ u2} α (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) (OfNat.ofNat.{u2} α 0 (Zero.toOfNat0.{u2} α (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))))
 Case conversion may be inaccurate. Consider using '#align matrix.det_ne_zero_of_left_inverse Matrix.det_ne_zero_of_left_inverseₓ'. -/
 theorem det_ne_zero_of_left_inverse [Nontrivial α] (h : B ⬝ A = 1) : A.det ≠ 0 :=
   (isUnit_det_of_left_inverse h).NeZero
@@ -410,7 +410,7 @@ theorem det_ne_zero_of_left_inverse [Nontrivial α] (h : B ⬝ A = 1) : A.det 
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {A : Matrix.{u1, u1, u2} n n α} {B : Matrix.{u1, u1, u2} n n α} [_inst_4 : Nontrivial.{u2} α], (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A B) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.one.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))))))) -> (Ne.{succ u2} α (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) (OfNat.ofNat.{u2} α 0 (OfNat.mk.{u2} α 0 (Zero.zero.{u2} α (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))))))))
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {A : Matrix.{u1, u1, u2} n n α} {B : Matrix.{u1, u1, u2} n n α} [_inst_4 : Nontrivial.{u2} α], (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A B) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))))) -> (Ne.{succ u2} α (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) (OfNat.ofNat.{u2} α 0 (Zero.toOfNat0.{u2} α (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))))
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {A : Matrix.{u1, u1, u2} n n α} {B : Matrix.{u1, u1, u2} n n α} [_inst_4 : Nontrivial.{u2} α], (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A B) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))))) -> (Ne.{succ u2} α (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) (OfNat.ofNat.{u2} α 0 (Zero.toOfNat0.{u2} α (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))))
 Case conversion may be inaccurate. Consider using '#align matrix.det_ne_zero_of_right_inverse Matrix.det_ne_zero_of_right_inverseₓ'. -/
 theorem det_ne_zero_of_right_inverse [Nontrivial α] (h : A ⬝ B = 1) : A.det ≠ 0 :=
   (isUnit_det_of_right_inverse h).NeZero
@@ -426,7 +426,7 @@ variable (A : Matrix n n α) (B : Matrix n n α)
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), (IsUnit.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (IsUnit.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 (Matrix.transpose.{u2, u1, u1} n n α A)))
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 (Matrix.transpose.{u2, u1, u1} n n α A)))
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 (Matrix.transpose.{u2, u1, u1} n n α A)))
 Case conversion may be inaccurate. Consider using '#align matrix.is_unit_det_transpose Matrix.isUnit_det_transposeₓ'. -/
 theorem isUnit_det_transpose (h : IsUnit A.det) : IsUnit Aᵀ.det :=
   by
@@ -445,7 +445,7 @@ noncomputable instance : Inv (Matrix n n α) :=
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) (SMul.smul.{u2, max u1 u2} α (Matrix.{u1, u1, u2} n n α) (Matrix.hasSmul.{u2, u1, u1, u2} n n α α (Mul.toSMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Ring.inverse.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) (Matrix.adjugate.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 A))
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) (HSMul.hSMul.{u2, max u1 u2, max u1 u2} α (Matrix.{u1, u1, u2} n n α) (Matrix.{u1, u1, u2} n n α) (instHSMul.{u2, max u1 u2} α (Matrix.{u1, u1, u2} n n α) (Matrix.smul.{u2, u1, u1, u2} n n α α (Algebra.toSMul.{u2, u2} α α (CommRing.toCommSemiring.{u2} α _inst_3) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Algebra.id.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Ring.inverse.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) (Matrix.adjugate.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 A))
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) (HSMul.hSMul.{u2, max u1 u2, max u1 u2} α (Matrix.{u1, u1, u2} n n α) (Matrix.{u1, u1, u2} n n α) (instHSMul.{u2, max u1 u2} α (Matrix.{u1, u1, u2} n n α) (Matrix.smul.{u2, u1, u1, u2} n n α α (Algebra.toSMul.{u2, u2} α α (CommRing.toCommSemiring.{u2} α _inst_3) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (Algebra.id.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Ring.inverse.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) (Matrix.adjugate.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 A))
 Case conversion may be inaccurate. Consider using '#align matrix.inv_def Matrix.inv_defₓ'. -/
 theorem inv_def (A : Matrix n n α) : A⁻¹ = Ring.inverse A.det • A.adjugate :=
   rfl
@@ -455,7 +455,7 @@ theorem inv_def (A : Matrix n n α) : A⁻¹ = Ring.inverse A.det • A.adjugate
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), (Not (IsUnit.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A))) -> (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 0 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 0 (Zero.zero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasZero.{u2, u1, u1} n n α (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))))))))
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), (Not (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A))) -> (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 0 (Zero.toOfNat0.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.zero.{u2, u1, u1} n n α (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))))
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), (Not (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A))) -> (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 0 (Zero.toOfNat0.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.zero.{u2, u1, u1} n n α (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))))
 Case conversion may be inaccurate. Consider using '#align matrix.nonsing_inv_apply_not_is_unit Matrix.nonsing_inv_apply_not_isUnitₓ'. -/
 theorem nonsing_inv_apply_not_isUnit (h : ¬IsUnit A.det) : A⁻¹ = 0 := by
   rw [inv_def, Ring.inverse_non_unit _ h, zero_smul]
@@ -465,7 +465,7 @@ theorem nonsing_inv_apply_not_isUnit (h : ¬IsUnit A.det) : A⁻¹ = 0 := by
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (h : IsUnit.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)), Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) (SMul.smul.{u2, max u1 u2} α (Matrix.{u1, u1, u2} n n α) (Matrix.hasSmul.{u2, u1, u1, u2} n n α α (Mul.toSMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Units.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3))) α (HasLiftT.mk.{succ u2, succ u2} (Units.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3))) α (CoeTCₓ.coe.{succ u2, succ u2} (Units.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3))) α (coeBase.{succ u2, succ u2} (Units.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3))) α (Units.hasCoe.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Inv.inv.{u2} (Units.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3))) (Units.hasInv.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3))) (IsUnit.unit.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) h))) (Matrix.adjugate.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 A))
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (h : IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)), Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) (HSMul.hSMul.{u2, max u1 u2, max u1 u2} α (Matrix.{u1, u1, u2} n n α) (Matrix.{u1, u1, u2} n n α) (instHSMul.{u2, max u1 u2} α (Matrix.{u1, u1, u2} n n α) (Matrix.smul.{u2, u1, u1, u2} n n α α (Algebra.toSMul.{u2, u2} α α (CommRing.toCommSemiring.{u2} α _inst_3) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Algebra.id.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Units.val.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Inv.inv.{u2} (Units.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Units.instInv.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (IsUnit.unit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) h))) (Matrix.adjugate.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 A))
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (h : IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)), Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) (HSMul.hSMul.{u2, max u1 u2, max u1 u2} α (Matrix.{u1, u1, u2} n n α) (Matrix.{u1, u1, u2} n n α) (instHSMul.{u2, max u1 u2} α (Matrix.{u1, u1, u2} n n α) (Matrix.smul.{u2, u1, u1, u2} n n α α (Algebra.toSMul.{u2, u2} α α (CommRing.toCommSemiring.{u2} α _inst_3) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (Algebra.id.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Units.val.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Inv.inv.{u2} (Units.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Units.instInv.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (IsUnit.unit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) h))) (Matrix.adjugate.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 A))
 Case conversion may be inaccurate. Consider using '#align matrix.nonsing_inv_apply Matrix.nonsing_inv_applyₓ'. -/
 theorem nonsing_inv_apply (h : IsUnit A.det) : A⁻¹ = (↑h.Unit⁻¹ : α) • A.adjugate := by
   rw [inv_def, ← Ring.inverse_unit h.unit, IsUnit.unit_spec]
@@ -475,7 +475,7 @@ theorem nonsing_inv_apply (h : IsUnit A.det) : A⁻¹ = (↑h.Unit⁻¹ : α) 
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) A], Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Invertible.invOf.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) A _inst_4) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) A], Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Invertible.invOf.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) A _inst_4) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) A], Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Invertible.invOf.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) A _inst_4) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)
 Case conversion may be inaccurate. Consider using '#align matrix.inv_of_eq_nonsing_inv Matrix.invOf_eq_nonsing_invₓ'. -/
 /-- The nonsingular inverse is the same as `inv_of` when `A` is invertible. -/
 @[simp]
@@ -489,7 +489,7 @@ theorem invOf_eq_nonsing_inv [Invertible A] : ⅟ A = A⁻¹ :=
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Units.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toRing.{u2} α _inst_3)))), Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) ((fun (a : Type.{max u1 u2}) (b : Type.{max u1 u2}) [self : HasLiftT.{succ (max u1 u2), succ (max u1 u2)} a b] => self.0) (Units.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toRing.{u2} α _inst_3)))) (Matrix.{u1, u1, u2} n n α) (HasLiftT.mk.{succ (max u1 u2), succ (max u1 u2)} (Units.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toRing.{u2} α _inst_3)))) (Matrix.{u1, u1, u2} n n α) (CoeTCₓ.coe.{succ (max u1 u2), succ (max u1 u2)} (Units.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toRing.{u2} α _inst_3)))) (Matrix.{u1, u1, u2} n n α) (coeBase.{succ (max u1 u2), succ (max u1 u2)} (Units.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toRing.{u2} α _inst_3)))) (Matrix.{u1, u1, u2} n n α) (Units.hasCoe.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toRing.{u2} α _inst_3))))))) (Inv.inv.{max u1 u2} (Units.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toRing.{u2} α _inst_3)))) (Units.hasInv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toRing.{u2} α _inst_3)))) A)) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) ((fun (a : Type.{max u1 u2}) (b : Type.{max u1 u2}) [self : HasLiftT.{succ (max u1 u2), succ (max u1 u2)} a b] => self.0) (Units.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toRing.{u2} α _inst_3)))) (Matrix.{u1, u1, u2} n n α) (HasLiftT.mk.{succ (max u1 u2), succ (max u1 u2)} (Units.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toRing.{u2} α _inst_3)))) (Matrix.{u1, u1, u2} n n α) (CoeTCₓ.coe.{succ (max u1 u2), succ (max u1 u2)} (Units.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toRing.{u2} α _inst_3)))) (Matrix.{u1, u1, u2} n n α) (coeBase.{succ (max u1 u2), succ (max u1 u2)} (Units.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toRing.{u2} α _inst_3)))) (Matrix.{u1, u1, u2} n n α) (Units.hasCoe.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toRing.{u2} α _inst_3))))))) A))
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Units.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) _inst_1 (fun (a : n) (b : n) => _inst_2 a b))))), Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Units.val.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) _inst_1 (fun (a : n) (b : n) => _inst_2 a b)))) (Inv.inv.{max u1 u2} (Units.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) _inst_1 (fun (a : n) (b : n) => _inst_2 a b))))) (Units.instInv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) _inst_1 (fun (a : n) (b : n) => _inst_2 a b))))) A)) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) (Units.val.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) _inst_1 (fun (a : n) (b : n) => _inst_2 a b)))) A))
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Units.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_1 (fun (a : n) (b : n) => _inst_2 a b))))), Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Units.val.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_1 (fun (a : n) (b : n) => _inst_2 a b)))) (Inv.inv.{max u1 u2} (Units.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_1 (fun (a : n) (b : n) => _inst_2 a b))))) (Units.instInv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_1 (fun (a : n) (b : n) => _inst_2 a b))))) A)) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) (Units.val.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_1 (fun (a : n) (b : n) => _inst_2 a b)))) A))
 Case conversion may be inaccurate. Consider using '#align matrix.coe_units_inv Matrix.coe_units_invₓ'. -/
 /-- Coercing the result of `units.has_inv` is the same as coercing first and applying the
 nonsingular inverse. -/
@@ -504,7 +504,7 @@ theorem coe_units_inv (A : (Matrix n n α)ˣ) : ↑A⁻¹ = (A⁻¹ : Matrix n n
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) (Ring.inverse.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) _inst_1 (fun (a : n) (b : n) => _inst_2 a b))) A)
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) (Ring.inverse.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) _inst_1 (fun (a : n) (b : n) => _inst_2 a b))) A)
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) (Ring.inverse.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_1 (fun (a : n) (b : n) => _inst_2 a b))) A)
 Case conversion may be inaccurate. Consider using '#align matrix.nonsing_inv_eq_ring_inverse Matrix.nonsing_inv_eq_ring_inverseₓ'. -/
 /-- The nonsingular inverse is the same as the general `ring.inverse`. -/
 theorem nonsing_inv_eq_ring_inverse : A⁻¹ = Ring.inverse A :=
@@ -530,7 +530,7 @@ theorem transpose_nonsing_inv : A⁻¹ᵀ = Aᵀ⁻¹ := by
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : StarRing.{u2} α (NonUnitalRing.toNonUnitalSemiring.{u2} α (NonUnitalCommRing.toNonUnitalRing.{u2} α (CommRing.toNonUnitalCommRing.{u2} α _inst_3)))], Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.conjTranspose.{u2, u1, u1} n n α (InvolutiveStar.toHasStar.{u2} α (StarAddMonoid.toHasInvolutiveStar.{u2} α (AddCommMonoid.toAddMonoid.{u2} α (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} α (NonUnitalRing.toNonUnitalSemiring.{u2} α (NonUnitalCommRing.toNonUnitalRing.{u2} α (CommRing.toNonUnitalCommRing.{u2} α _inst_3)))))) (StarRing.toStarAddMonoid.{u2} α (NonUnitalRing.toNonUnitalSemiring.{u2} α (NonUnitalCommRing.toNonUnitalRing.{u2} α (CommRing.toNonUnitalCommRing.{u2} α _inst_3))) _inst_4))) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) (Matrix.conjTranspose.{u2, u1, u1} n n α (InvolutiveStar.toHasStar.{u2} α (StarAddMonoid.toHasInvolutiveStar.{u2} α (AddCommMonoid.toAddMonoid.{u2} α (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} α (NonUnitalRing.toNonUnitalSemiring.{u2} α (NonUnitalCommRing.toNonUnitalRing.{u2} α (CommRing.toNonUnitalCommRing.{u2} α _inst_3)))))) (StarRing.toStarAddMonoid.{u2} α (NonUnitalRing.toNonUnitalSemiring.{u2} α (NonUnitalCommRing.toNonUnitalRing.{u2} α (CommRing.toNonUnitalCommRing.{u2} α _inst_3))) _inst_4))) A))
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : StarRing.{u2} α (NonUnitalRing.toNonUnitalSemiring.{u2} α (NonUnitalCommRing.toNonUnitalRing.{u2} α (CommRing.toNonUnitalCommRing.{u2} α _inst_3)))], Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.conjTranspose.{u2, u1, u1} n n α (InvolutiveStar.toStar.{u2} α (StarAddMonoid.toInvolutiveStar.{u2} α (AddMonoidWithOne.toAddMonoid.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (Ring.toAddGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (StarRing.toStarAddMonoid.{u2} α (NonUnitalRing.toNonUnitalSemiring.{u2} α (NonUnitalCommRing.toNonUnitalRing.{u2} α (CommRing.toNonUnitalCommRing.{u2} α _inst_3))) _inst_4))) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) (Matrix.conjTranspose.{u2, u1, u1} n n α (InvolutiveStar.toStar.{u2} α (StarAddMonoid.toInvolutiveStar.{u2} α (AddMonoidWithOne.toAddMonoid.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (Ring.toAddGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (StarRing.toStarAddMonoid.{u2} α (NonUnitalRing.toNonUnitalSemiring.{u2} α (NonUnitalCommRing.toNonUnitalRing.{u2} α (CommRing.toNonUnitalCommRing.{u2} α _inst_3))) _inst_4))) A))
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : StarRing.{u2} α (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} α (NonUnitalCommRing.toNonUnitalCommSemiring.{u2} α (CommRing.toNonUnitalCommRing.{u2} α _inst_3)))], Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.conjTranspose.{u2, u1, u1} n n α (InvolutiveStar.toStar.{u2} α (StarAddMonoid.toInvolutiveStar.{u2} α (AddMonoidWithOne.toAddMonoid.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (Ring.toAddGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (StarRing.toStarAddMonoid.{u2} α (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} α (NonUnitalCommRing.toNonUnitalCommSemiring.{u2} α (CommRing.toNonUnitalCommRing.{u2} α _inst_3))) _inst_4))) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) (Matrix.conjTranspose.{u2, u1, u1} n n α (InvolutiveStar.toStar.{u2} α (StarAddMonoid.toInvolutiveStar.{u2} α (AddMonoidWithOne.toAddMonoid.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (Ring.toAddGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (StarRing.toStarAddMonoid.{u2} α (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} α (NonUnitalCommRing.toNonUnitalCommSemiring.{u2} α (CommRing.toNonUnitalCommRing.{u2} α _inst_3))) _inst_4))) A))
 Case conversion may be inaccurate. Consider using '#align matrix.conj_transpose_nonsing_inv Matrix.conjTranspose_nonsing_invₓ'. -/
 theorem conjTranspose_nonsing_inv [StarRing α] : A⁻¹ᴴ = Aᴴ⁻¹ := by
   rw [inv_def, inv_def, conj_transpose_smul, det_conj_transpose, adjugate_conj_transpose,
@@ -541,7 +541,7 @@ theorem conjTranspose_nonsing_inv [StarRing α] : A⁻¹ᴴ = Aᴴ⁻¹ := by
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), (IsUnit.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.one.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3))))))))))
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))))
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))))
 Case conversion may be inaccurate. Consider using '#align matrix.mul_nonsing_inv Matrix.mul_nonsing_invₓ'. -/
 /-- The `nonsing_inv` of `A` is a right inverse. -/
 @[simp]
@@ -555,7 +555,7 @@ theorem mul_nonsing_inv (h : IsUnit A.det) : A ⬝ A⁻¹ = 1 :=
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), (IsUnit.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.one.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3))))))))))
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))))
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))))
 Case conversion may be inaccurate. Consider using '#align matrix.nonsing_inv_mul Matrix.nonsing_inv_mulₓ'. -/
 /-- The `nonsing_inv` of `A` is a left inverse. -/
 @[simp]
@@ -574,7 +574,7 @@ instance [Invertible A] : Invertible A⁻¹ :=
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) A], Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)) A
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) A], Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)) A
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) A], Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)) A
 Case conversion may be inaccurate. Consider using '#align matrix.inv_inv_of_invertible Matrix.inv_inv_of_invertibleₓ'. -/
 @[simp]
 theorem inv_inv_of_invertible [Invertible A] : A⁻¹⁻¹ = A := by
@@ -585,7 +585,7 @@ theorem inv_inv_of_invertible [Invertible A] : A⁻¹⁻¹ = A := by
 lean 3 declaration is
   forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] (A : Matrix.{u2, u2, u3} n n α) (B : Matrix.{u1, u2, u3} m n α), (IsUnit.{u3} α (Ring.toMonoid.{u3} α (CommRing.toRing.{u3} α _inst_3)) (Matrix.det.{u3, u2} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{succ (max u1 u2 u3)} (Matrix.{u1, u2, u3} m n α) (Matrix.mul.{u3, u1, u2, u2} m n n α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) (Matrix.mul.{u3, u1, u2, u2} m n n α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) B A) (Inv.inv.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.hasInv.{u2, u3} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)) B)
 but is expected to have type
-  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] (A : Matrix.{u2, u2, u3} n n α) (B : Matrix.{u1, u2, u3} m n α), (IsUnit.{u3} α (MonoidWithZero.toMonoid.{u3} α (Semiring.toMonoidWithZero.{u3} α (Ring.toSemiring.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (Matrix.det.{u3, u2} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{max (max (succ u1) (succ u2)) (succ u3)} (Matrix.{u1, u2, u3} m n α) (Matrix.mul.{u3, u1, u2, u2} m n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) (Matrix.mul.{u3, u1, u2, u2} m n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) B A) (Inv.inv.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.inv.{u2, u3} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)) B)
+  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] (A : Matrix.{u2, u2, u3} n n α) (B : Matrix.{u1, u2, u3} m n α), (IsUnit.{u3} α (MonoidWithZero.toMonoid.{u3} α (Semiring.toMonoidWithZero.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) (Matrix.det.{u3, u2} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{max (max (succ u1) (succ u2)) (succ u3)} (Matrix.{u1, u2, u3} m n α) (Matrix.mul.{u3, u1, u2, u2} m n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) (Matrix.mul.{u3, u1, u2, u2} m n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) B A) (Inv.inv.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.inv.{u2, u3} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)) B)
 Case conversion may be inaccurate. Consider using '#align matrix.mul_nonsing_inv_cancel_right Matrix.mul_nonsing_inv_cancel_rightₓ'. -/
 @[simp]
 theorem mul_nonsing_inv_cancel_right (B : Matrix m n α) (h : IsUnit A.det) : B ⬝ A ⬝ A⁻¹ = B := by
@@ -596,7 +596,7 @@ theorem mul_nonsing_inv_cancel_right (B : Matrix m n α) (h : IsUnit A.det) : B
 lean 3 declaration is
   forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] (A : Matrix.{u2, u2, u3} n n α) (B : Matrix.{u2, u1, u3} n m α), (IsUnit.{u3} α (Ring.toMonoid.{u3} α (CommRing.toRing.{u3} α _inst_3)) (Matrix.det.{u3, u2} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{succ (max u2 u1 u3)} (Matrix.{u2, u1, u3} n m α) (Matrix.mul.{u3, u2, u2, u1} n n m α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) A (Matrix.mul.{u3, u2, u2, u1} n n m α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) (Inv.inv.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.hasInv.{u2, u3} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) B)) B)
 but is expected to have type
-  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] (A : Matrix.{u2, u2, u3} n n α) (B : Matrix.{u2, u1, u3} n m α), (IsUnit.{u3} α (MonoidWithZero.toMonoid.{u3} α (Semiring.toMonoidWithZero.{u3} α (Ring.toSemiring.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (Matrix.det.{u3, u2} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{max (max (succ u1) (succ u2)) (succ u3)} (Matrix.{u2, u1, u3} n m α) (Matrix.mul.{u3, u2, u2, u1} n n m α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) A (Matrix.mul.{u3, u2, u2, u1} n n m α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) (Inv.inv.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.inv.{u2, u3} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) B)) B)
+  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] (A : Matrix.{u2, u2, u3} n n α) (B : Matrix.{u2, u1, u3} n m α), (IsUnit.{u3} α (MonoidWithZero.toMonoid.{u3} α (Semiring.toMonoidWithZero.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) (Matrix.det.{u3, u2} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{max (max (succ u1) (succ u2)) (succ u3)} (Matrix.{u2, u1, u3} n m α) (Matrix.mul.{u3, u2, u2, u1} n n m α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) A (Matrix.mul.{u3, u2, u2, u1} n n m α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) (Inv.inv.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.inv.{u2, u3} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) B)) B)
 Case conversion may be inaccurate. Consider using '#align matrix.mul_nonsing_inv_cancel_left Matrix.mul_nonsing_inv_cancel_leftₓ'. -/
 @[simp]
 theorem mul_nonsing_inv_cancel_left (B : Matrix n m α) (h : IsUnit A.det) : A ⬝ (A⁻¹ ⬝ B) = B := by
@@ -607,7 +607,7 @@ theorem mul_nonsing_inv_cancel_left (B : Matrix n m α) (h : IsUnit A.det) : A 
 lean 3 declaration is
   forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] (A : Matrix.{u2, u2, u3} n n α) (B : Matrix.{u1, u2, u3} m n α), (IsUnit.{u3} α (Ring.toMonoid.{u3} α (CommRing.toRing.{u3} α _inst_3)) (Matrix.det.{u3, u2} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{succ (max u1 u2 u3)} (Matrix.{u1, u2, u3} m n α) (Matrix.mul.{u3, u1, u2, u2} m n n α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) (Matrix.mul.{u3, u1, u2, u2} m n n α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) B (Inv.inv.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.hasInv.{u2, u3} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)) A) B)
 but is expected to have type
-  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] (A : Matrix.{u2, u2, u3} n n α) (B : Matrix.{u1, u2, u3} m n α), (IsUnit.{u3} α (MonoidWithZero.toMonoid.{u3} α (Semiring.toMonoidWithZero.{u3} α (Ring.toSemiring.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (Matrix.det.{u3, u2} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{max (max (succ u1) (succ u2)) (succ u3)} (Matrix.{u1, u2, u3} m n α) (Matrix.mul.{u3, u1, u2, u2} m n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) (Matrix.mul.{u3, u1, u2, u2} m n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) B (Inv.inv.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.inv.{u2, u3} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)) A) B)
+  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] (A : Matrix.{u2, u2, u3} n n α) (B : Matrix.{u1, u2, u3} m n α), (IsUnit.{u3} α (MonoidWithZero.toMonoid.{u3} α (Semiring.toMonoidWithZero.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) (Matrix.det.{u3, u2} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{max (max (succ u1) (succ u2)) (succ u3)} (Matrix.{u1, u2, u3} m n α) (Matrix.mul.{u3, u1, u2, u2} m n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) (Matrix.mul.{u3, u1, u2, u2} m n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) B (Inv.inv.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.inv.{u2, u3} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)) A) B)
 Case conversion may be inaccurate. Consider using '#align matrix.nonsing_inv_mul_cancel_right Matrix.nonsing_inv_mul_cancel_rightₓ'. -/
 @[simp]
 theorem nonsing_inv_mul_cancel_right (B : Matrix m n α) (h : IsUnit A.det) : B ⬝ A⁻¹ ⬝ A = B := by
@@ -618,7 +618,7 @@ theorem nonsing_inv_mul_cancel_right (B : Matrix m n α) (h : IsUnit A.det) : B
 lean 3 declaration is
   forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] (A : Matrix.{u2, u2, u3} n n α) (B : Matrix.{u2, u1, u3} n m α), (IsUnit.{u3} α (Ring.toMonoid.{u3} α (CommRing.toRing.{u3} α _inst_3)) (Matrix.det.{u3, u2} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{succ (max u2 u1 u3)} (Matrix.{u2, u1, u3} n m α) (Matrix.mul.{u3, u2, u2, u1} n n m α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) (Inv.inv.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.hasInv.{u2, u3} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) (Matrix.mul.{u3, u2, u2, u1} n n m α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) A B)) B)
 but is expected to have type
-  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] (A : Matrix.{u2, u2, u3} n n α) (B : Matrix.{u2, u1, u3} n m α), (IsUnit.{u3} α (MonoidWithZero.toMonoid.{u3} α (Semiring.toMonoidWithZero.{u3} α (Ring.toSemiring.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (Matrix.det.{u3, u2} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{max (max (succ u1) (succ u2)) (succ u3)} (Matrix.{u2, u1, u3} n m α) (Matrix.mul.{u3, u2, u2, u1} n n m α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) (Inv.inv.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.inv.{u2, u3} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) (Matrix.mul.{u3, u2, u2, u1} n n m α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) A B)) B)
+  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] (A : Matrix.{u2, u2, u3} n n α) (B : Matrix.{u2, u1, u3} n m α), (IsUnit.{u3} α (MonoidWithZero.toMonoid.{u3} α (Semiring.toMonoidWithZero.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) (Matrix.det.{u3, u2} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{max (max (succ u1) (succ u2)) (succ u3)} (Matrix.{u2, u1, u3} n m α) (Matrix.mul.{u3, u2, u2, u1} n n m α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) (Inv.inv.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.inv.{u2, u3} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) (Matrix.mul.{u3, u2, u2, u1} n n m α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) A B)) B)
 Case conversion may be inaccurate. Consider using '#align matrix.nonsing_inv_mul_cancel_left Matrix.nonsing_inv_mul_cancel_leftₓ'. -/
 @[simp]
 theorem nonsing_inv_mul_cancel_left (B : Matrix n m α) (h : IsUnit A.det) : A⁻¹ ⬝ (A ⬝ B) = B := by
@@ -629,7 +629,7 @@ theorem nonsing_inv_mul_cancel_left (B : Matrix n m α) (h : IsUnit A.det) : A
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) A], Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.one.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))))))
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) A], Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))))
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) A], Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))))
 Case conversion may be inaccurate. Consider using '#align matrix.mul_inv_of_invertible Matrix.mul_inv_of_invertibleₓ'. -/
 @[simp]
 theorem mul_inv_of_invertible [Invertible A] : A ⬝ A⁻¹ = 1 :=
@@ -640,7 +640,7 @@ theorem mul_inv_of_invertible [Invertible A] : A ⬝ A⁻¹ = 1 :=
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) A], Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.one.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))))))
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) A], Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))))
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) A], Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))))
 Case conversion may be inaccurate. Consider using '#align matrix.inv_mul_of_invertible Matrix.inv_mul_of_invertibleₓ'. -/
 @[simp]
 theorem inv_mul_of_invertible [Invertible A] : A⁻¹ ⬝ A = 1 :=
@@ -651,7 +651,7 @@ theorem inv_mul_of_invertible [Invertible A] : A⁻¹ ⬝ A = 1 :=
 lean 3 declaration is
   forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] (A : Matrix.{u2, u2, u3} n n α) (B : Matrix.{u1, u2, u3} m n α) [_inst_4 : Invertible.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.hasMul.{u3, u2} n α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.hasOne.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u3} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (AddMonoidWithOne.toOne.{u3} α (AddGroupWithOne.toAddMonoidWithOne.{u3} α (AddCommGroupWithOne.toAddGroupWithOne.{u3} α (Ring.toAddCommGroupWithOne.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) A], Eq.{succ (max u1 u2 u3)} (Matrix.{u1, u2, u3} m n α) (Matrix.mul.{u3, u1, u2, u2} m n n α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) (Matrix.mul.{u3, u1, u2, u2} m n n α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) B A) (Inv.inv.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.hasInv.{u2, u3} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)) B
 but is expected to have type
-  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] (A : Matrix.{u2, u2, u3} n n α) (B : Matrix.{u1, u2, u3} m n α) [_inst_4 : Invertible.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.instMulMatrix.{u3, u2} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (NonAssocRing.toOne.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) A], Eq.{max (max (succ u1) (succ u2)) (succ u3)} (Matrix.{u1, u2, u3} m n α) (Matrix.mul.{u3, u1, u2, u2} m n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) (Matrix.mul.{u3, u1, u2, u2} m n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) B A) (Inv.inv.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.inv.{u2, u3} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)) B
+  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] (A : Matrix.{u2, u2, u3} n n α) (B : Matrix.{u1, u2, u3} m n α) [_inst_4 : Invertible.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.instMulMatrix.{u3, u2} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (Semiring.toOne.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) A], Eq.{max (max (succ u1) (succ u2)) (succ u3)} (Matrix.{u1, u2, u3} m n α) (Matrix.mul.{u3, u1, u2, u2} m n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) (Matrix.mul.{u3, u1, u2, u2} m n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) B A) (Inv.inv.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.inv.{u2, u3} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)) B
 Case conversion may be inaccurate. Consider using '#align matrix.mul_inv_cancel_right_of_invertible Matrix.mul_inv_cancel_right_of_invertibleₓ'. -/
 @[simp]
 theorem mul_inv_cancel_right_of_invertible (B : Matrix m n α) [Invertible A] : B ⬝ A ⬝ A⁻¹ = B :=
@@ -662,7 +662,7 @@ theorem mul_inv_cancel_right_of_invertible (B : Matrix m n α) [Invertible A] :
 lean 3 declaration is
   forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] (A : Matrix.{u2, u2, u3} n n α) (B : Matrix.{u2, u1, u3} n m α) [_inst_4 : Invertible.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.hasMul.{u3, u2} n α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.hasOne.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u3} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (AddMonoidWithOne.toOne.{u3} α (AddGroupWithOne.toAddMonoidWithOne.{u3} α (AddCommGroupWithOne.toAddGroupWithOne.{u3} α (Ring.toAddCommGroupWithOne.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) A], Eq.{succ (max u2 u1 u3)} (Matrix.{u2, u1, u3} n m α) (Matrix.mul.{u3, u2, u2, u1} n n m α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) A (Matrix.mul.{u3, u2, u2, u1} n n m α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) (Inv.inv.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.hasInv.{u2, u3} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) B)) B
 but is expected to have type
-  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] (A : Matrix.{u2, u2, u3} n n α) (B : Matrix.{u2, u1, u3} n m α) [_inst_4 : Invertible.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.instMulMatrix.{u3, u2} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (NonAssocRing.toOne.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) A], Eq.{max (max (succ u1) (succ u2)) (succ u3)} (Matrix.{u2, u1, u3} n m α) (Matrix.mul.{u3, u2, u2, u1} n n m α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) A (Matrix.mul.{u3, u2, u2, u1} n n m α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) (Inv.inv.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.inv.{u2, u3} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) B)) B
+  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] (A : Matrix.{u2, u2, u3} n n α) (B : Matrix.{u2, u1, u3} n m α) [_inst_4 : Invertible.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.instMulMatrix.{u3, u2} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (Semiring.toOne.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) A], Eq.{max (max (succ u1) (succ u2)) (succ u3)} (Matrix.{u2, u1, u3} n m α) (Matrix.mul.{u3, u2, u2, u1} n n m α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) A (Matrix.mul.{u3, u2, u2, u1} n n m α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) (Inv.inv.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.inv.{u2, u3} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) B)) B
 Case conversion may be inaccurate. Consider using '#align matrix.mul_inv_cancel_left_of_invertible Matrix.mul_inv_cancel_left_of_invertibleₓ'. -/
 @[simp]
 theorem mul_inv_cancel_left_of_invertible (B : Matrix n m α) [Invertible A] : A ⬝ (A⁻¹ ⬝ B) = B :=
@@ -673,7 +673,7 @@ theorem mul_inv_cancel_left_of_invertible (B : Matrix n m α) [Invertible A] : A
 lean 3 declaration is
   forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] (A : Matrix.{u2, u2, u3} n n α) (B : Matrix.{u1, u2, u3} m n α) [_inst_4 : Invertible.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.hasMul.{u3, u2} n α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.hasOne.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u3} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (AddMonoidWithOne.toOne.{u3} α (AddGroupWithOne.toAddMonoidWithOne.{u3} α (AddCommGroupWithOne.toAddGroupWithOne.{u3} α (Ring.toAddCommGroupWithOne.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) A], Eq.{succ (max u1 u2 u3)} (Matrix.{u1, u2, u3} m n α) (Matrix.mul.{u3, u1, u2, u2} m n n α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) (Matrix.mul.{u3, u1, u2, u2} m n n α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) B (Inv.inv.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.hasInv.{u2, u3} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)) A) B
 but is expected to have type
-  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] (A : Matrix.{u2, u2, u3} n n α) (B : Matrix.{u1, u2, u3} m n α) [_inst_4 : Invertible.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.instMulMatrix.{u3, u2} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (NonAssocRing.toOne.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) A], Eq.{max (max (succ u1) (succ u2)) (succ u3)} (Matrix.{u1, u2, u3} m n α) (Matrix.mul.{u3, u1, u2, u2} m n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) (Matrix.mul.{u3, u1, u2, u2} m n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) B (Inv.inv.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.inv.{u2, u3} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)) A) B
+  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] (A : Matrix.{u2, u2, u3} n n α) (B : Matrix.{u1, u2, u3} m n α) [_inst_4 : Invertible.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.instMulMatrix.{u3, u2} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (Semiring.toOne.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) A], Eq.{max (max (succ u1) (succ u2)) (succ u3)} (Matrix.{u1, u2, u3} m n α) (Matrix.mul.{u3, u1, u2, u2} m n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) (Matrix.mul.{u3, u1, u2, u2} m n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) B (Inv.inv.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.inv.{u2, u3} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)) A) B
 Case conversion may be inaccurate. Consider using '#align matrix.inv_mul_cancel_right_of_invertible Matrix.inv_mul_cancel_right_of_invertibleₓ'. -/
 @[simp]
 theorem inv_mul_cancel_right_of_invertible (B : Matrix m n α) [Invertible A] : B ⬝ A⁻¹ ⬝ A = B :=
@@ -684,7 +684,7 @@ theorem inv_mul_cancel_right_of_invertible (B : Matrix m n α) [Invertible A] :
 lean 3 declaration is
   forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] (A : Matrix.{u2, u2, u3} n n α) (B : Matrix.{u2, u1, u3} n m α) [_inst_4 : Invertible.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.hasMul.{u3, u2} n α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.hasOne.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u3} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (AddMonoidWithOne.toOne.{u3} α (AddGroupWithOne.toAddMonoidWithOne.{u3} α (AddCommGroupWithOne.toAddGroupWithOne.{u3} α (Ring.toAddCommGroupWithOne.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) A], Eq.{succ (max u2 u1 u3)} (Matrix.{u2, u1, u3} n m α) (Matrix.mul.{u3, u2, u2, u1} n n m α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) (Inv.inv.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.hasInv.{u2, u3} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) (Matrix.mul.{u3, u2, u2, u1} n n m α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) A B)) B
 but is expected to have type
-  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] (A : Matrix.{u2, u2, u3} n n α) (B : Matrix.{u2, u1, u3} n m α) [_inst_4 : Invertible.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.instMulMatrix.{u3, u2} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (NonAssocRing.toOne.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) A], Eq.{max (max (succ u1) (succ u2)) (succ u3)} (Matrix.{u2, u1, u3} n m α) (Matrix.mul.{u3, u2, u2, u1} n n m α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) (Inv.inv.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.inv.{u2, u3} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) (Matrix.mul.{u3, u2, u2, u1} n n m α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) A B)) B
+  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] (A : Matrix.{u2, u2, u3} n n α) (B : Matrix.{u2, u1, u3} n m α) [_inst_4 : Invertible.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.instMulMatrix.{u3, u2} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (Semiring.toOne.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) A], Eq.{max (max (succ u1) (succ u2)) (succ u3)} (Matrix.{u2, u1, u3} n m α) (Matrix.mul.{u3, u2, u2, u1} n n m α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) (Inv.inv.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.inv.{u2, u3} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) (Matrix.mul.{u3, u2, u2, u1} n n m α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) A B)) B
 Case conversion may be inaccurate. Consider using '#align matrix.inv_mul_cancel_left_of_invertible Matrix.inv_mul_cancel_left_of_invertibleₓ'. -/
 @[simp]
 theorem inv_mul_cancel_left_of_invertible (B : Matrix n m α) [Invertible A] : A⁻¹ ⬝ (A ⬝ B) = B :=
@@ -695,7 +695,7 @@ theorem inv_mul_cancel_left_of_invertible (B : Matrix n m α) [Invertible A] : A
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (B : Matrix.{u1, u1, u2} n n α) (C : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) A], Iff (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) B) C) (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) B (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A C))
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (B : Matrix.{u1, u1, u2} n n α) (C : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) A], Iff (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) B) C) (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) B (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A C))
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (B : Matrix.{u1, u1, u2} n n α) (C : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) A], Iff (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) B) C) (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) B (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A C))
 Case conversion may be inaccurate. Consider using '#align matrix.inv_mul_eq_iff_eq_mul_of_invertible Matrix.inv_mul_eq_iff_eq_mul_of_invertibleₓ'. -/
 theorem inv_mul_eq_iff_eq_mul_of_invertible (A B C : Matrix n n α) [Invertible A] :
     A⁻¹ ⬝ B = C ↔ B = A ⬝ C :=
@@ -707,7 +707,7 @@ theorem inv_mul_eq_iff_eq_mul_of_invertible (A B C : Matrix n n α) [Invertible
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (B : Matrix.{u1, u1, u2} n n α) (C : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) A], Iff (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) B (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)) C) (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) B (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) C A))
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (B : Matrix.{u1, u1, u2} n n α) (C : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) A], Iff (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) B (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)) C) (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) B (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) C A))
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (B : Matrix.{u1, u1, u2} n n α) (C : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) A], Iff (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) B (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)) C) (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) B (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) C A))
 Case conversion may be inaccurate. Consider using '#align matrix.mul_inv_eq_iff_eq_mul_of_invertible Matrix.mul_inv_eq_iff_eq_mul_of_invertibleₓ'. -/
 theorem mul_inv_eq_iff_eq_mul_of_invertible (A B C : Matrix n n α) [Invertible A] :
     B ⬝ A⁻¹ = C ↔ B = C ⬝ A :=
@@ -719,7 +719,7 @@ theorem mul_inv_eq_iff_eq_mul_of_invertible (A B C : Matrix n n α) [Invertible
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), Or (And (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.one.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))))))) (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.one.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3))))))))))) (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 0 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 0 (Zero.zero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasZero.{u2, u1, u1} n n α (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))))))))
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), Or (And (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))))) (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))))) (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 0 (Zero.toOfNat0.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.zero.{u2, u1, u1} n n α (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))))
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), Or (And (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))))) (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))))) (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 0 (Zero.toOfNat0.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.zero.{u2, u1, u1} n n α (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))))
 Case conversion may be inaccurate. Consider using '#align matrix.nonsing_inv_cancel_or_zero Matrix.nonsing_inv_cancel_or_zeroₓ'. -/
 theorem nonsing_inv_cancel_or_zero : A⁻¹ ⬝ A = 1 ∧ A ⬝ A⁻¹ = 1 ∨ A⁻¹ = 0 :=
   by
@@ -732,7 +732,7 @@ theorem nonsing_inv_cancel_or_zero : A⁻¹ ⬝ A = 1 ∧ A ⬝ A⁻¹ = 1 ∨ A
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), (IsUnit.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{succ u2} α (HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) (OfNat.ofNat.{u2} α 1 (OfNat.mk.{u2} α 1 (One.one.{u2} α (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))))))
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{succ u2} α (HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) (OfNat.ofNat.{u2} α 1 (One.toOfNat1.{u2} α (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))))
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{succ u2} α (HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) (OfNat.ofNat.{u2} α 1 (One.toOfNat1.{u2} α (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))))
 Case conversion may be inaccurate. Consider using '#align matrix.det_nonsing_inv_mul_det Matrix.det_nonsing_inv_mul_detₓ'. -/
 theorem det_nonsing_inv_mul_det (h : IsUnit A.det) : A⁻¹.det * A.det = 1 := by
   rw [← det_mul, A.nonsing_inv_mul h, det_one]
@@ -742,7 +742,7 @@ theorem det_nonsing_inv_mul_det (h : IsUnit A.det) : A⁻¹.det * A.det = 1 := b
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), Eq.{succ u2} α (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)) (Ring.inverse.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A))
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), Eq.{succ u2} α (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)) (Ring.inverse.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A))
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), Eq.{succ u2} α (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)) (Ring.inverse.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A))
 Case conversion may be inaccurate. Consider using '#align matrix.det_nonsing_inv Matrix.det_nonsing_invₓ'. -/
 @[simp]
 theorem det_nonsing_inv : A⁻¹.det = Ring.inverse A.det :=
@@ -760,7 +760,7 @@ theorem det_nonsing_inv : A⁻¹.det = Ring.inverse A.det :=
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), (IsUnit.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (IsUnit.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)))
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)))
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)))
 Case conversion may be inaccurate. Consider using '#align matrix.is_unit_nonsing_inv_det Matrix.isUnit_nonsing_inv_detₓ'. -/
 theorem isUnit_nonsing_inv_det (h : IsUnit A.det) : IsUnit A⁻¹.det :=
   isUnit_of_mul_eq_one _ _ (A.det_nonsing_inv_mul_det h)
@@ -770,7 +770,7 @@ theorem isUnit_nonsing_inv_det (h : IsUnit A.det) : IsUnit A⁻¹.det :=
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), (IsUnit.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)) A)
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)) A)
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)) A)
 Case conversion may be inaccurate. Consider using '#align matrix.nonsing_inv_nonsing_inv Matrix.nonsing_inv_nonsing_invₓ'. -/
 @[simp]
 theorem nonsing_inv_nonsing_inv (h : IsUnit A.det) : A⁻¹⁻¹ = A :=
@@ -786,7 +786,7 @@ theorem nonsing_inv_nonsing_inv (h : IsUnit A.det) : A⁻¹⁻¹ = A :=
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {A : Matrix.{u1, u1, u2} n n α}, Iff (IsUnit.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A))) (IsUnit.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A))
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {A : Matrix.{u1, u1, u2} n n α}, Iff (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A))) (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A))
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {A : Matrix.{u1, u1, u2} n n α}, Iff (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A))) (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A))
 Case conversion may be inaccurate. Consider using '#align matrix.is_unit_nonsing_inv_det_iff Matrix.isUnit_nonsing_inv_det_iffₓ'. -/
 theorem isUnit_nonsing_inv_det_iff {A : Matrix n n α} : IsUnit A⁻¹.det ↔ IsUnit A.det := by
   rw [Matrix.det_nonsing_inv, isUnit_ring_inverse]
@@ -796,7 +796,7 @@ theorem isUnit_nonsing_inv_det_iff {A : Matrix n n α} : IsUnit A⁻¹.det ↔ I
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), (IsUnit.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) A)
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) A)
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) A)
 Case conversion may be inaccurate. Consider using '#align matrix.invertible_of_is_unit_det Matrix.invertibleOfIsUnitDetₓ'. -/
 -- `is_unit.invertible` lifts the proposition `is_unit A` to a constructive inverse of `A`.
 /-- A version of `matrix.invertible_of_det_invertible` with the inverse defeq to `A⁻¹` that is
@@ -809,7 +809,7 @@ noncomputable def invertibleOfIsUnitDet (h : IsUnit A.det) : Invertible A :=
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), (IsUnit.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Units.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toRing.{u2} α _inst_3))))
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Units.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) _inst_1 (fun (a : n) (b : n) => _inst_2 a b)))))
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Units.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_1 (fun (a : n) (b : n) => _inst_2 a b)))))
 Case conversion may be inaccurate. Consider using '#align matrix.nonsing_inv_unit Matrix.nonsingInvUnitₓ'. -/
 /-- A version of `matrix.units_of_det_invertible` with the inverse defeq to `A⁻¹` that is therefore
 noncomputable. -/
@@ -821,7 +821,7 @@ noncomputable def nonsingInvUnit (h : IsUnit A.det) : (Matrix n n α)ˣ :=
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)], Eq.{succ (max u1 u2)} (Units.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toRing.{u2} α _inst_3)))) (Matrix.unitOfDetInvertible.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3 A _inst_4) (Matrix.nonsingInvUnit.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3 A (isUnit_of_invertible.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) _inst_4))
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{u2} α (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)], Eq.{max (succ u1) (succ u2)} (Units.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) _inst_1 (fun (a : n) (b : n) => _inst_2 a b))))) (Matrix.unitOfDetInvertible.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3 A _inst_4) (Matrix.nonsingInvUnit.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3 A (isUnit_of_invertible.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) _inst_4))
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{u2} α (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)], Eq.{max (succ u1) (succ u2)} (Units.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_1 (fun (a : n) (b : n) => _inst_2 a b))))) (Matrix.unitOfDetInvertible.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3 A _inst_4) (Matrix.nonsingInvUnit.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3 A (isUnit_of_invertible.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) _inst_4))
 Case conversion may be inaccurate. Consider using '#align matrix.unit_of_det_invertible_eq_nonsing_inv_unit Matrix.unitOfDetInvertible_eq_nonsingInvUnitₓ'. -/
 theorem unitOfDetInvertible_eq_nonsingInvUnit [Invertible A.det] :
     unitOfDetInvertible A = nonsingInvUnit A (isUnit_of_invertible _) :=
@@ -836,7 +836,7 @@ variable {A} {B}
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {A : Matrix.{u1, u1, u2} n n α} {B : Matrix.{u1, u1, u2} n n α}, (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) B A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.one.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))))))) -> (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) B)
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {A : Matrix.{u1, u1, u2} n n α} {B : Matrix.{u1, u1, u2} n n α}, (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) B A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))))) -> (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) B)
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {A : Matrix.{u1, u1, u2} n n α} {B : Matrix.{u1, u1, u2} n n α}, (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) B A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))))) -> (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) B)
 Case conversion may be inaccurate. Consider using '#align matrix.inv_eq_left_inv Matrix.inv_eq_left_invₓ'. -/
 /-- If matrix A is left invertible, then its inverse equals its left inverse. -/
 theorem inv_eq_left_inv (h : B ⬝ A = 1) : A⁻¹ = B :=
@@ -848,7 +848,7 @@ theorem inv_eq_left_inv (h : B ⬝ A = 1) : A⁻¹ = B :=
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {A : Matrix.{u1, u1, u2} n n α} {B : Matrix.{u1, u1, u2} n n α}, (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A B) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.one.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))))))) -> (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) B)
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {A : Matrix.{u1, u1, u2} n n α} {B : Matrix.{u1, u1, u2} n n α}, (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A B) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))))) -> (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) B)
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {A : Matrix.{u1, u1, u2} n n α} {B : Matrix.{u1, u1, u2} n n α}, (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A B) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))))) -> (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) B)
 Case conversion may be inaccurate. Consider using '#align matrix.inv_eq_right_inv Matrix.inv_eq_right_invₓ'. -/
 /-- If matrix A is right invertible, then its inverse equals its right inverse. -/
 theorem inv_eq_right_inv (h : A ⬝ B = 1) : A⁻¹ = B :=
@@ -863,7 +863,7 @@ variable {C : Matrix n n α}
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {A : Matrix.{u1, u1, u2} n n α} {B : Matrix.{u1, u1, u2} n n α} {C : Matrix.{u1, u1, u2} n n α}, (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) B A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.one.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))))))) -> (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) C A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.one.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))))))) -> (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) B C)
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {A : Matrix.{u1, u1, u2} n n α} {B : Matrix.{u1, u1, u2} n n α} {C : Matrix.{u1, u1, u2} n n α}, (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) B A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))))) -> (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) C A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))))) -> (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) B C)
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {A : Matrix.{u1, u1, u2} n n α} {B : Matrix.{u1, u1, u2} n n α} {C : Matrix.{u1, u1, u2} n n α}, (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) B A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))))) -> (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) C A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))))) -> (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) B C)
 Case conversion may be inaccurate. Consider using '#align matrix.left_inv_eq_left_inv Matrix.left_inv_eq_left_invₓ'. -/
 /-- The left inverse of matrix A is unique when existing. -/
 theorem left_inv_eq_left_inv (h : B ⬝ A = 1) (g : C ⬝ A = 1) : B = C := by
@@ -874,7 +874,7 @@ theorem left_inv_eq_left_inv (h : B ⬝ A = 1) (g : C ⬝ A = 1) : B = C := by
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {A : Matrix.{u1, u1, u2} n n α} {B : Matrix.{u1, u1, u2} n n α} {C : Matrix.{u1, u1, u2} n n α}, (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A B) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.one.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))))))) -> (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A C) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.one.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))))))) -> (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) B C)
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {A : Matrix.{u1, u1, u2} n n α} {B : Matrix.{u1, u1, u2} n n α} {C : Matrix.{u1, u1, u2} n n α}, (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A B) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))))) -> (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A C) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))))) -> (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) B C)
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {A : Matrix.{u1, u1, u2} n n α} {B : Matrix.{u1, u1, u2} n n α} {C : Matrix.{u1, u1, u2} n n α}, (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A B) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))))) -> (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A C) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))))) -> (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) B C)
 Case conversion may be inaccurate. Consider using '#align matrix.right_inv_eq_right_inv Matrix.right_inv_eq_right_invₓ'. -/
 /-- The right inverse of matrix A is unique when existing. -/
 theorem right_inv_eq_right_inv (h : A ⬝ B = 1) (g : A ⬝ C = 1) : B = C := by
@@ -885,7 +885,7 @@ theorem right_inv_eq_right_inv (h : A ⬝ B = 1) (g : A ⬝ C = 1) : B = C := by
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {A : Matrix.{u1, u1, u2} n n α} {B : Matrix.{u1, u1, u2} n n α} {C : Matrix.{u1, u1, u2} n n α}, (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A B) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.one.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))))))) -> (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) C A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.one.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))))))) -> (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) B C)
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {A : Matrix.{u1, u1, u2} n n α} {B : Matrix.{u1, u1, u2} n n α} {C : Matrix.{u1, u1, u2} n n α}, (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A B) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))))) -> (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) C A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))))) -> (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) B C)
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {A : Matrix.{u1, u1, u2} n n α} {B : Matrix.{u1, u1, u2} n n α} {C : Matrix.{u1, u1, u2} n n α}, (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A B) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))))) -> (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) C A) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.toOfNat1.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))))) -> (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) B C)
 Case conversion may be inaccurate. Consider using '#align matrix.right_inv_eq_left_inv Matrix.right_inv_eq_left_invₓ'. -/
 /-- The right inverse of matrix A equals the left inverse of A when they exist. -/
 theorem right_inv_eq_left_inv (h : A ⬝ B = 1) (g : C ⬝ A = 1) : B = C := by
@@ -896,7 +896,7 @@ theorem right_inv_eq_left_inv (h : A ⬝ B = 1) (g : C ⬝ A = 1) : B = C := by
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {A : Matrix.{u1, u1, u2} n n α} {B : Matrix.{u1, u1, u2} n n α}, (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) B)) -> (IsUnit.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) A B)
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {A : Matrix.{u1, u1, u2} n n α} {B : Matrix.{u1, u1, u2} n n α}, (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) B)) -> (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) A B)
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {A : Matrix.{u1, u1, u2} n n α} {B : Matrix.{u1, u1, u2} n n α}, (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) B)) -> (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) A B)
 Case conversion may be inaccurate. Consider using '#align matrix.inv_inj Matrix.inv_injₓ'. -/
 theorem inv_inj (h : A⁻¹ = B⁻¹) (h' : IsUnit A.det) : A = B :=
   by
@@ -938,7 +938,7 @@ noncomputable instance : InvOneClass (Matrix n n α) :=
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (k : α) [_inst_4 : Invertible.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3))))) k], (IsUnit.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) (SMul.smul.{u2, max u1 u2} α (Matrix.{u1, u1, u2} n n α) (Matrix.hasSmul.{u2, u1, u1, u2} n n α α (Mul.toSMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))))) k A)) (SMul.smul.{u2, max u1 u2} α (Matrix.{u1, u1, u2} n n α) (Matrix.hasSmul.{u2, u1, u1, u2} n n α α (Mul.toSMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Invertible.invOf.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3))))) k _inst_4) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)))
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (k : α) [_inst_4 : Invertible.{u2} α (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))) k], (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) (HSMul.hSMul.{u2, max u1 u2, max u1 u2} α (Matrix.{u1, u1, u2} n n α) (Matrix.{u1, u1, u2} n n α) (instHSMul.{u2, max u1 u2} α (Matrix.{u1, u1, u2} n n α) (Matrix.smul.{u2, u1, u1, u2} n n α α (Algebra.toSMul.{u2, u2} α α (CommRing.toCommSemiring.{u2} α _inst_3) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Algebra.id.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) k A)) (HSMul.hSMul.{u2, max u1 u2, max u1 u2} α (Matrix.{u1, u1, u2} n n α) (Matrix.{u1, u1, u2} n n α) (instHSMul.{u2, max u1 u2} α (Matrix.{u1, u1, u2} n n α) (Matrix.smul.{u2, u1, u1, u2} n n α α (Algebra.toSMul.{u2, u2} α α (CommRing.toCommSemiring.{u2} α _inst_3) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Algebra.id.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Invertible.invOf.{u2} α (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))) k _inst_4) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)))
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (k : α) [_inst_4 : Invertible.{u2} α (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) k], (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) (HSMul.hSMul.{u2, max u1 u2, max u1 u2} α (Matrix.{u1, u1, u2} n n α) (Matrix.{u1, u1, u2} n n α) (instHSMul.{u2, max u1 u2} α (Matrix.{u1, u1, u2} n n α) (Matrix.smul.{u2, u1, u1, u2} n n α α (Algebra.toSMul.{u2, u2} α α (CommRing.toCommSemiring.{u2} α _inst_3) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (Algebra.id.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) k A)) (HSMul.hSMul.{u2, max u1 u2, max u1 u2} α (Matrix.{u1, u1, u2} n n α) (Matrix.{u1, u1, u2} n n α) (instHSMul.{u2, max u1 u2} α (Matrix.{u1, u1, u2} n n α) (Matrix.smul.{u2, u1, u1, u2} n n α α (Algebra.toSMul.{u2, u2} α α (CommRing.toCommSemiring.{u2} α _inst_3) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (Algebra.id.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Invertible.invOf.{u2} α (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) k _inst_4) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)))
 Case conversion may be inaccurate. Consider using '#align matrix.inv_smul Matrix.inv_smulₓ'. -/
 theorem inv_smul (k : α) [Invertible k] (h : IsUnit A.det) : (k • A)⁻¹ = ⅟ k • A⁻¹ :=
   inv_eq_left_inv (by simp [h, smul_smul])
@@ -948,7 +948,7 @@ theorem inv_smul (k : α) [Invertible k] (h : IsUnit A.det) : (k • A)⁻¹ = 
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (k : Units.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3))), (IsUnit.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) (SMul.smul.{u2, max u1 u2} (Units.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3))) (Matrix.{u1, u1, u2} n n α) (Matrix.hasSmul.{u2, u1, u1, u2} n n (Units.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3))) α (Units.hasSmul.{u2, u2} α α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Mul.toSMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) k A)) (SMul.smul.{u2, max u1 u2} (Units.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3))) (Matrix.{u1, u1, u2} n n α) (Matrix.hasSmul.{u2, u1, u1, u2} n n (Units.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3))) α (Units.hasSmul.{u2, u2} α α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Mul.toSMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Inv.inv.{u2} (Units.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3))) (Units.hasInv.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3))) k) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)))
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (k : Units.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))), (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) (HSMul.hSMul.{u2, max u1 u2, max u1 u2} (Units.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.{u1, u1, u2} n n α) (Matrix.{u1, u1, u2} n n α) (instHSMul.{u2, max u1 u2} (Units.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.{u1, u1, u2} n n α) (Units.instSMulUnits.{u2, max u1 u2} α (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.smul.{u2, u1, u1, u2} n n α α (Algebra.toSMul.{u2, u2} α α (CommRing.toCommSemiring.{u2} α _inst_3) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Algebra.id.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))) k A)) (HSMul.hSMul.{u2, max u1 u2, max u1 u2} (Units.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.{u1, u1, u2} n n α) (Matrix.{u1, u1, u2} n n α) (instHSMul.{u2, max u1 u2} (Units.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.{u1, u1, u2} n n α) (Units.instSMulUnits.{u2, max u1 u2} α (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.smul.{u2, u1, u1, u2} n n α α (Algebra.toSMul.{u2, u2} α α (CommRing.toCommSemiring.{u2} α _inst_3) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Algebra.id.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))) (Inv.inv.{u2} (Units.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Units.instInv.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) k) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)))
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (k : Units.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))), (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) (HSMul.hSMul.{u2, max u1 u2, max u1 u2} (Units.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Matrix.{u1, u1, u2} n n α) (Matrix.{u1, u1, u2} n n α) (instHSMul.{u2, max u1 u2} (Units.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Matrix.{u1, u1, u2} n n α) (Units.instSMulUnits.{u2, max u1 u2} α (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Matrix.smul.{u2, u1, u1, u2} n n α α (Algebra.toSMul.{u2, u2} α α (CommRing.toCommSemiring.{u2} α _inst_3) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (Algebra.id.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))) k A)) (HSMul.hSMul.{u2, max u1 u2, max u1 u2} (Units.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Matrix.{u1, u1, u2} n n α) (Matrix.{u1, u1, u2} n n α) (instHSMul.{u2, max u1 u2} (Units.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Matrix.{u1, u1, u2} n n α) (Units.instSMulUnits.{u2, max u1 u2} α (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Matrix.smul.{u2, u1, u1, u2} n n α α (Algebra.toSMul.{u2, u2} α α (CommRing.toCommSemiring.{u2} α _inst_3) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (Algebra.id.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))) (Inv.inv.{u2} (Units.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Units.instInv.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) k) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)))
 Case conversion may be inaccurate. Consider using '#align matrix.inv_smul' Matrix.inv_smul'ₓ'. -/
 theorem inv_smul' (k : αˣ) (h : IsUnit A.det) : (k • A)⁻¹ = k⁻¹ • A⁻¹ :=
   inv_eq_left_inv (by simp [h, smul_smul])
@@ -958,7 +958,7 @@ theorem inv_smul' (k : αˣ) (h : IsUnit A.det) : (k • A)⁻¹ = k⁻¹ • A
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (h : IsUnit.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)), Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) (Matrix.adjugate.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 A)) (SMul.smul.{u2, max u1 u2} (Units.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3))) (Matrix.{u1, u1, u2} n n α) (Matrix.hasSmul.{u2, u1, u1, u2} n n (Units.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3))) α (Units.hasSmul.{u2, u2} α α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Mul.toSMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Inv.inv.{u2} (Units.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3))) (Units.hasInv.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3))) (IsUnit.unit.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) h)) A)
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (h : IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)), Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) (Matrix.adjugate.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 A)) (HSMul.hSMul.{u2, max u1 u2, max u1 u2} (Units.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.{u1, u1, u2} n n α) (Matrix.{u1, u1, u2} n n α) (instHSMul.{u2, max u1 u2} (Units.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.{u1, u1, u2} n n α) (Units.instSMulUnits.{u2, max u1 u2} α (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.smul.{u2, u1, u1, u2} n n α α (Algebra.toSMul.{u2, u2} α α (CommRing.toCommSemiring.{u2} α _inst_3) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Algebra.id.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))) (Inv.inv.{u2} (Units.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Units.instInv.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (IsUnit.unit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) h)) A)
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (h : IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)), Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) (Matrix.adjugate.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 A)) (HSMul.hSMul.{u2, max u1 u2, max u1 u2} (Units.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Matrix.{u1, u1, u2} n n α) (Matrix.{u1, u1, u2} n n α) (instHSMul.{u2, max u1 u2} (Units.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Matrix.{u1, u1, u2} n n α) (Units.instSMulUnits.{u2, max u1 u2} α (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Matrix.smul.{u2, u1, u1, u2} n n α α (Algebra.toSMul.{u2, u2} α α (CommRing.toCommSemiring.{u2} α _inst_3) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (Algebra.id.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))) (Inv.inv.{u2} (Units.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Units.instInv.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (IsUnit.unit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) h)) A)
 Case conversion may be inaccurate. Consider using '#align matrix.inv_adjugate Matrix.inv_adjugateₓ'. -/
 theorem inv_adjugate (A : Matrix n n α) (h : IsUnit A.det) : (adjugate A)⁻¹ = h.Unit⁻¹ • A :=
   by
@@ -998,7 +998,7 @@ theorem invOf_diagonal_eq {α} [Semiring α] (v : n → α) [Invertible v] [Inve
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (v : n -> α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.diagonal.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) v)], Invertible.{max u1 u2} (n -> α) (Pi.instMul.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Pi.instOne.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) v
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (v : n -> α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.diagonal.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) v)], Invertible.{max u1 u2} (n -> α) (Pi.instMul.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Pi.instOne.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) v
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (v : n -> α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Matrix.diagonal.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) v)], Invertible.{max u1 u2} (n -> α) (Pi.instMul.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Pi.instOne.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) v
 Case conversion may be inaccurate. Consider using '#align matrix.invertible_of_diagonal_invertible Matrix.invertibleOfDiagonalInvertibleₓ'. -/
 /-- `v` is invertible if `diagonal v` is -/
 def invertibleOfDiagonalInvertible (v : n → α) [Invertible (diagonal v)] : Invertible v
@@ -1026,7 +1026,7 @@ def invertibleOfDiagonalInvertible (v : n → α) [Invertible (diagonal v)] : In
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (v : n -> α), Equiv.{succ (max u1 u2), succ (max u1 u2)} (Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.diagonal.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) v)) (Invertible.{max u1 u2} (n -> α) (Pi.instMul.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Pi.instOne.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) v)
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (v : n -> α), Equiv.{succ (max u1 u2), succ (max u1 u2)} (Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.diagonal.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) v)) (Invertible.{max u1 u2} (n -> α) (Pi.instMul.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Pi.instOne.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) v)
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (v : n -> α), Equiv.{succ (max u1 u2), succ (max u1 u2)} (Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Matrix.diagonal.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) v)) (Invertible.{max u1 u2} (n -> α) (Pi.instMul.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Pi.instOne.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) v)
 Case conversion may be inaccurate. Consider using '#align matrix.diagonal_invertible_equiv_invertible Matrix.diagonalInvertibleEquivInvertibleₓ'. -/
 /-- Together `matrix.diagonal_invertible` and `matrix.invertible_of_diagonal_invertible` form an
 equivalence, although both sides of the equiv are subsingleton anyway. -/
@@ -1043,7 +1043,7 @@ def diagonalInvertibleEquivInvertible (v : n → α) : Invertible (diagonal v) 
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {v : n -> α}, Iff (IsUnit.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toRing.{u2} α _inst_3))) (Matrix.diagonal.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) v)) (IsUnit.{max u1 u2} (n -> α) (Pi.monoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3))) v)
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {v : n -> α}, Iff (IsUnit.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) _inst_1 (fun (a : n) (b : n) => _inst_2 a b)))) (Matrix.diagonal.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) v)) (IsUnit.{max u1 u2} (n -> α) (Pi.monoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) v)
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {v : n -> α}, Iff (IsUnit.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_1 (fun (a : n) (b : n) => _inst_2 a b)))) (Matrix.diagonal.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) v)) (IsUnit.{max u1 u2} (n -> α) (Pi.monoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) v)
 Case conversion may be inaccurate. Consider using '#align matrix.is_unit_diagonal Matrix.isUnit_diagonalₓ'. -/
 /-- When lowered to a prop, `matrix.diagonal_invertible_equiv_invertible` forms an `iff`. -/
 @[simp]
@@ -1056,7 +1056,7 @@ theorem isUnit_diagonal {v : n → α} : IsUnit (diagonal v) ↔ IsUnit v := by
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (v : n -> α), Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) (Matrix.diagonal.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) v)) (Matrix.diagonal.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Ring.inverse.{max u1 u2} (n -> α) (Pi.monoidWithZero.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) v))
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (v : n -> α), Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) (Matrix.diagonal.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) v)) (Matrix.diagonal.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Ring.inverse.{max u1 u2} (n -> α) (Pi.monoidWithZero.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) v))
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (v : n -> α), Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) (Matrix.diagonal.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) v)) (Matrix.diagonal.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Ring.inverse.{max u1 u2} (n -> α) (Pi.monoidWithZero.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) v))
 Case conversion may be inaccurate. Consider using '#align matrix.inv_diagonal Matrix.inv_diagonalₓ'. -/
 theorem inv_diagonal (v : n → α) : (diagonal v)⁻¹ = diagonal (Ring.inverse v) :=
   by
@@ -1103,7 +1103,7 @@ theorem mul_inv_rev (A B : Matrix n n α) : (A ⬝ B)⁻¹ = B⁻¹ ⬝ A⁻¹ :
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (l : List.{max u1 u2} (Matrix.{u1, u1, u2} n n α)), Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) (List.prod.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) l)) (List.prod.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (List.map.{max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3)) (List.reverse.{max u1 u2} (Matrix.{u1, u1, u2} n n α) l)))
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (l : List.{max u2 u1} (Matrix.{u1, u1, u2} n n α)), Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) (List.prod.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) l)) (List.prod.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (List.map.{max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3)) (List.reverse.{max u1 u2} (Matrix.{u1, u1, u2} n n α) l)))
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (l : List.{max u2 u1} (Matrix.{u1, u1, u2} n n α)), Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) (List.prod.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) l)) (List.prod.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (Semiring.toOne.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (List.map.{max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3)) (List.reverse.{max u1 u2} (Matrix.{u1, u1, u2} n n α) l)))
 Case conversion may be inaccurate. Consider using '#align matrix.list_prod_inv_reverse Matrix.list_prod_inv_reverseₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- A version of `list.prod_inv_reverse` for `matrix.has_inv`. -/
@@ -1118,7 +1118,7 @@ theorem list_prod_inv_reverse : ∀ l : List (Matrix n n α), l.Prod⁻¹ = (l.r
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (b : n -> α), (IsUnit.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{succ (max u1 u2)} (n -> α) (SMul.smul.{u2, max u1 u2} α (n -> α) (Function.hasSMul.{u1, u2, u2} n α α (Mul.toSMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) (Matrix.mulVec.{u2, u1, u1} n n α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) _inst_1 (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) b)) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u2, u2, max u1 u2, max u1 u2} α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (n -> α) (n -> α) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.Function.module.{u1, u2, u2} n α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Pi.Function.module.{u1, u2, u2} n α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (_x : LinearMap.{u2, u2, max u1 u2, max u1 u2} α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (n -> α) (n -> α) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.Function.module.{u1, u2, u2} n α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Pi.Function.module.{u1, u2, u2} n α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) => (n -> α) -> n -> α) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, max u1 u2} α α (n -> α) (n -> α) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.Function.module.{u1, u2, u2} n α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Pi.Function.module.{u1, u2, u2} n α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.cramer.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 A) b))
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (b : n -> α), (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{max (succ u1) (succ u2)} (n -> α) (HSMul.hSMul.{u2, max u1 u2, max u1 u2} α (n -> α) (n -> α) (instHSMul.{u2, max u1 u2} α (n -> α) (Pi.instSMul.{u1, u2, u2} n α (fun (a._@.Mathlib.Data.Matrix.Basic._hyg.18074 : n) => α) (fun (i : n) => Algebra.toSMul.{u2, u2} α α (CommRing.toCommSemiring.{u2} α _inst_3) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Algebra.id.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) (Matrix.mulVec.{u2, u1, u1} n n α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) _inst_1 (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) b)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u2, u2, max u1 u2, max u1 u2} α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (RingHom.id.{u2} α (NonAssocRing.toNonAssocSemiring.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (n -> α) (n -> α) (Pi.addCommMonoid.{u1, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (n -> α) (fun (_x : n -> α) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : n -> α) => n -> α) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, max u1 u2} α α (n -> α) (n -> α) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (RingHom.id.{u2} α (NonAssocRing.toNonAssocSemiring.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.cramer.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 A) b))
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (b : n -> α), (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{max (succ u1) (succ u2)} (n -> α) (HSMul.hSMul.{u2, max u1 u2, max u1 u2} α (n -> α) (n -> α) (instHSMul.{u2, max u1 u2} α (n -> α) (Pi.instSMul.{u1, u2, u2} n α (fun (a._@.Mathlib.Data.Matrix.Basic._hyg.18074 : n) => α) (fun (i : n) => Algebra.toSMul.{u2, u2} α α (CommRing.toCommSemiring.{u2} α _inst_3) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (Algebra.id.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) (Matrix.mulVec.{u2, u1, u1} n n α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) _inst_1 (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) b)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u2, u2, max u1 u2, max u1 u2} α α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (n -> α) (n -> α) (Pi.addCommMonoid.{u1, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (n -> α) (fun (_x : n -> α) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : n -> α) => n -> α) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, max u1 u2} α α (n -> α) (n -> α) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Matrix.cramer.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 A) b))
 Case conversion may be inaccurate. Consider using '#align matrix.det_smul_inv_mul_vec_eq_cramer Matrix.det_smul_inv_mulVec_eq_cramerₓ'. -/
 /-- One form of **Cramer's rule**. See `matrix.mul_vec_cramer` for a stronger form. -/
 @[simp]
@@ -1132,7 +1132,7 @@ theorem det_smul_inv_mulVec_eq_cramer (A : Matrix n n α) (b : n → α) (h : Is
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (b : n -> α), (IsUnit.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{succ (max u1 u2)} (n -> α) (SMul.smul.{u2, max u1 u2} α (n -> α) (Function.hasSMul.{u1, u2, u2} n α α (Mul.toSMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) (Matrix.vecMul.{u2, u1, u1} n n α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) _inst_1 b (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A))) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u2, u2, max u1 u2, max u1 u2} α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (n -> α) (n -> α) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.Function.module.{u1, u2, u2} n α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Pi.Function.module.{u1, u2, u2} n α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (_x : LinearMap.{u2, u2, max u1 u2, max u1 u2} α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (n -> α) (n -> α) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.Function.module.{u1, u2, u2} n α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Pi.Function.module.{u1, u2, u2} n α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) => (n -> α) -> n -> α) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, max u1 u2} α α (n -> α) (n -> α) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.Function.module.{u1, u2, u2} n α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Pi.Function.module.{u1, u2, u2} n α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.cramer.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 (Matrix.transpose.{u2, u1, u1} n n α A)) b))
 but is expected to have type
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(NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) _inst_1 b (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u2, u2, max u1 u2, max u1 u2} α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (RingHom.id.{u2} α (NonAssocRing.toNonAssocSemiring.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (n -> α) (n -> α) (Pi.addCommMonoid.{u1, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (n -> α) (fun (_x : n -> α) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : n -> α) => n -> α) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, max u1 u2} α α (n -> α) (n -> α) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (RingHom.id.{u2} α (NonAssocRing.toNonAssocSemiring.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.cramer.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 (Matrix.transpose.{u2, u1, u1} n n α A)) b))
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (b : n -> α), (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{max (succ u1) (succ u2)} (n -> α) (HSMul.hSMul.{u2, max u1 u2, max u1 u2} α (n -> α) (n -> α) (instHSMul.{u2, max u1 u2} α (n -> α) (Pi.instSMul.{u1, u2, u2} n α (fun (a._@.Mathlib.Data.Matrix.Basic._hyg.18132 : n) => α) (fun (i : n) => Algebra.toSMul.{u2, u2} α α (CommRing.toCommSemiring.{u2} α _inst_3) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (Algebra.id.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) (Matrix.vecMul.{u2, u1, u1} n n α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) _inst_1 b (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u2, u2, max u1 u2, max u1 u2} α α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (n -> α) (n -> α) (Pi.addCommMonoid.{u1, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (n -> α) (fun (_x : n -> α) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : n -> α) => n -> α) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, max u1 u2} α α (n -> α) (n -> α) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Matrix.cramer.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 (Matrix.transpose.{u2, u1, u1} n n α A)) b))
 Case conversion may be inaccurate. Consider using '#align matrix.det_smul_inv_vec_mul_eq_cramer_transpose Matrix.det_smul_inv_vecMul_eq_cramer_transposeₓ'. -/
 /-- One form of **Cramer's rule**. See `matrix.mul_vec_cramer` for a stronger form. -/
 @[simp]
@@ -1159,7 +1159,7 @@ variable [DecidableEq m]
 lean 3 declaration is
   forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] [_inst_4 : Fintype.{u1} m] [_inst_5 : DecidableEq.{succ u1} m] (A : Matrix.{u1, u1, u3} m m α) (e₁ : Equiv.{succ u2, succ u1} n m) (e₂ : Equiv.{succ u2, succ u1} n m) [_inst_6 : Invertible.{max u1 u3} (Matrix.{u1, u1, u3} m m α) (Matrix.hasMul.{u3, u1} m α _inst_4 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.hasOne.{u3, u1} m α (fun (a : m) (b : m) => _inst_5 a b) (MulZeroClass.toHasZero.{u3} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (AddMonoidWithOne.toOne.{u3} α (AddGroupWithOne.toAddMonoidWithOne.{u3} α (AddCommGroupWithOne.toAddGroupWithOne.{u3} α (Ring.toAddCommGroupWithOne.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) A], Invertible.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.hasMul.{u3, u2} n α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.hasOne.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u3} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (AddMonoidWithOne.toOne.{u3} α (AddGroupWithOne.toAddMonoidWithOne.{u3} α (AddCommGroupWithOne.toAddGroupWithOne.{u3} α (Ring.toAddCommGroupWithOne.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.submatrix.{u3, u2, u1, u1, u2} n m m n α A (coeFn.{max 1 (max (succ u2) (succ u1)) (succ u1) (succ u2), max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} n m) (fun (_x : Equiv.{succ u2, succ u1} n m) => n -> m) (Equiv.hasCoeToFun.{succ u2, succ u1} n m) e₁) (coeFn.{max 1 (max (succ u2) (succ u1)) (succ u1) (succ u2), max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} n m) (fun (_x : Equiv.{succ u2, succ u1} n m) => n -> m) (Equiv.hasCoeToFun.{succ u2, succ u1} n m) e₂))
 but is expected to have type
-  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] [_inst_4 : Fintype.{u1} m] [_inst_5 : DecidableEq.{succ u1} m] (A : Matrix.{u1, u1, u3} m m α) (e₁ : Equiv.{succ u2, succ u1} n m) (e₂ : Equiv.{succ u2, succ u1} n m) [_inst_6 : Invertible.{max u1 u3} (Matrix.{u1, u1, u3} m m α) (Matrix.instMulMatrix.{u3, u1} m α _inst_4 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u1} m α (fun (a : m) (b : m) => _inst_5 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (NonAssocRing.toOne.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) A], Invertible.{max u3 u2} (Matrix.{u2, u2, u3} n n α) (Matrix.instMulMatrix.{u3, u2} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (NonAssocRing.toOne.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (Matrix.submatrix.{u3, u2, u1, u1, u2} n m m n α A (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₁) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₂))
+  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] [_inst_4 : Fintype.{u1} m] [_inst_5 : DecidableEq.{succ u1} m] (A : Matrix.{u1, u1, u3} m m α) (e₁ : Equiv.{succ u2, succ u1} n m) (e₂ : Equiv.{succ u2, succ u1} n m) [_inst_6 : Invertible.{max u1 u3} (Matrix.{u1, u1, u3} m m α) (Matrix.instMulMatrix.{u3, u1} m α _inst_4 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u1} m α (fun (a : m) (b : m) => _inst_5 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (Semiring.toOne.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) A], Invertible.{max u3 u2} (Matrix.{u2, u2, u3} n n α) (Matrix.instMulMatrix.{u3, u2} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (Semiring.toOne.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) (Matrix.submatrix.{u3, u2, u1, u1, u2} n m m n α A (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₁) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₂))
 Case conversion may be inaccurate. Consider using '#align matrix.submatrix_equiv_invertible Matrix.submatrixEquivInvertibleₓ'. -/
 /-- `A.submatrix e₁ e₂` is invertible if `A` is -/
 def submatrixEquivInvertible (A : Matrix m m α) (e₁ e₂ : n ≃ m) [Invertible A] :
@@ -1172,7 +1172,7 @@ def submatrixEquivInvertible (A : Matrix m m α) (e₁ e₂ : n ≃ m) [Invertib
 lean 3 declaration is
   forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] [_inst_4 : Fintype.{u1} m] [_inst_5 : DecidableEq.{succ u1} m] (A : Matrix.{u1, u1, u3} m m α) (e₁ : Equiv.{succ u2, succ u1} n m) (e₂ : Equiv.{succ u2, succ u1} n m) [_inst_6 : Invertible.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.hasMul.{u3, u2} n α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.hasOne.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u3} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (AddMonoidWithOne.toOne.{u3} α (AddGroupWithOne.toAddMonoidWithOne.{u3} α (AddCommGroupWithOne.toAddGroupWithOne.{u3} α (Ring.toAddCommGroupWithOne.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.submatrix.{u3, u2, u1, u1, u2} n m m n α A (coeFn.{max 1 (max (succ u2) (succ u1)) (succ u1) (succ u2), max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} n m) (fun (_x : Equiv.{succ u2, succ u1} n m) => n -> m) (Equiv.hasCoeToFun.{succ u2, succ u1} n m) e₁) (coeFn.{max 1 (max (succ u2) (succ u1)) (succ u1) (succ u2), max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} n m) (fun (_x : Equiv.{succ u2, succ u1} n m) => n -> m) (Equiv.hasCoeToFun.{succ u2, succ u1} n m) e₂))], Invertible.{max u1 u3} (Matrix.{u1, u1, u3} m m α) (Matrix.hasMul.{u3, u1} m α _inst_4 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.hasOne.{u3, u1} m α (fun (a : m) (b : m) => _inst_5 a b) (MulZeroClass.toHasZero.{u3} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (AddMonoidWithOne.toOne.{u3} α (AddGroupWithOne.toAddMonoidWithOne.{u3} α (AddCommGroupWithOne.toAddGroupWithOne.{u3} α (Ring.toAddCommGroupWithOne.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) A
 but is expected to have type
-  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] [_inst_4 : Fintype.{u1} m] [_inst_5 : DecidableEq.{succ u1} m] (A : Matrix.{u1, u1, u3} m m α) (e₁ : Equiv.{succ u2, succ u1} n m) (e₂ : Equiv.{succ u2, succ u1} n m) [_inst_6 : Invertible.{max u3 u2} (Matrix.{u2, u2, u3} n n α) (Matrix.instMulMatrix.{u3, u2} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (NonAssocRing.toOne.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (Matrix.submatrix.{u3, u2, u1, u1, u2} n m m n α A (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₁) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₂))], Invertible.{max u1 u3} (Matrix.{u1, u1, u3} m m α) (Matrix.instMulMatrix.{u3, u1} m α _inst_4 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u1} m α (fun (a : m) (b : m) => _inst_5 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (NonAssocRing.toOne.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) A
+  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] [_inst_4 : Fintype.{u1} m] [_inst_5 : DecidableEq.{succ u1} m] (A : Matrix.{u1, u1, u3} m m α) (e₁ : Equiv.{succ u2, succ u1} n m) (e₂ : Equiv.{succ u2, succ u1} n m) [_inst_6 : Invertible.{max u3 u2} (Matrix.{u2, u2, u3} n n α) (Matrix.instMulMatrix.{u3, u2} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (Semiring.toOne.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) (Matrix.submatrix.{u3, u2, u1, u1, u2} n m m n α A (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₁) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₂))], Invertible.{max u1 u3} (Matrix.{u1, u1, u3} m m α) (Matrix.instMulMatrix.{u3, u1} m α _inst_4 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u1} m α (fun (a : m) (b : m) => _inst_5 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (Semiring.toOne.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) A
 Case conversion may be inaccurate. Consider using '#align matrix.invertible_of_submatrix_equiv_invertible Matrix.invertibleOfSubmatrixEquivInvertibleₓ'. -/
 /-- `A` is invertible if `A.submatrix e₁ e₂` is -/
 def invertibleOfSubmatrixEquivInvertible (A : Matrix m m α) (e₁ e₂ : n ≃ m)
@@ -1190,7 +1190,7 @@ def invertibleOfSubmatrixEquivInvertible (A : Matrix m m α) (e₁ e₂ : n ≃
 lean 3 declaration is
   forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] [_inst_4 : Fintype.{u1} m] [_inst_5 : DecidableEq.{succ u1} m] (A : Matrix.{u1, u1, u3} m m α) (e₁ : Equiv.{succ u2, succ u1} n m) (e₂ : Equiv.{succ u2, succ u1} n m) [_inst_6 : Invertible.{max u1 u3} (Matrix.{u1, u1, u3} m m α) (Matrix.hasMul.{u3, u1} m α _inst_4 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.hasOne.{u3, u1} m α (fun (a : m) (b : m) => _inst_5 a b) (MulZeroClass.toHasZero.{u3} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (AddMonoidWithOne.toOne.{u3} α (AddGroupWithOne.toAddMonoidWithOne.{u3} α (AddCommGroupWithOne.toAddGroupWithOne.{u3} α (Ring.toAddCommGroupWithOne.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) A] [_inst_7 : Invertible.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.hasMul.{u3, u2} n α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.hasOne.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u3} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (AddMonoidWithOne.toOne.{u3} α (AddGroupWithOne.toAddMonoidWithOne.{u3} α (AddCommGroupWithOne.toAddGroupWithOne.{u3} α (Ring.toAddCommGroupWithOne.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.submatrix.{u3, u2, u1, u1, u2} n m m n α A (coeFn.{max 1 (max (succ u2) (succ u1)) (succ u1) (succ u2), max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} n m) (fun (_x : Equiv.{succ u2, succ u1} n m) => n -> m) (Equiv.hasCoeToFun.{succ u2, succ u1} n m) e₁) (coeFn.{max 1 (max (succ u2) (succ u1)) (succ u1) (succ u2), max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} n m) (fun (_x : Equiv.{succ u2, succ u1} n m) => n -> m) (Equiv.hasCoeToFun.{succ u2, succ u1} n m) e₂))], Eq.{succ (max u2 u3)} (Matrix.{u2, u2, u3} n n α) (Invertible.invOf.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.hasMul.{u3, u2} n α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.hasOne.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u3} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (AddMonoidWithOne.toOne.{u3} α (AddGroupWithOne.toAddMonoidWithOne.{u3} α (AddCommGroupWithOne.toAddGroupWithOne.{u3} α (Ring.toAddCommGroupWithOne.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.submatrix.{u3, u2, u1, u1, u2} n m m n α A (coeFn.{max 1 (max (succ u2) (succ u1)) (succ u1) (succ u2), max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} n m) (fun (_x : Equiv.{succ u2, succ u1} n m) => n -> m) (Equiv.hasCoeToFun.{succ u2, succ u1} n m) e₁) (coeFn.{max 1 (max (succ u2) (succ u1)) (succ u1) (succ u2), max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} n m) (fun (_x : Equiv.{succ u2, succ u1} n m) => n -> m) (Equiv.hasCoeToFun.{succ u2, succ u1} n m) e₂)) _inst_7) (Matrix.submatrix.{u3, u2, u1, u1, u2} n m m n α (Invertible.invOf.{max u1 u3} (Matrix.{u1, u1, u3} m m α) (Matrix.hasMul.{u3, u1} m α _inst_4 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.hasOne.{u3, u1} m α (fun (a : m) (b : m) => _inst_5 a b) (MulZeroClass.toHasZero.{u3} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (AddMonoidWithOne.toOne.{u3} α (AddGroupWithOne.toAddMonoidWithOne.{u3} α (AddCommGroupWithOne.toAddGroupWithOne.{u3} α (Ring.toAddCommGroupWithOne.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) A _inst_6) 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 but is expected to have type
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+  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] [_inst_4 : Fintype.{u1} m] [_inst_5 : DecidableEq.{succ u1} m] (A : Matrix.{u1, u1, u3} m m α) (e₁ : Equiv.{succ u2, succ u1} n m) (e₂ : Equiv.{succ u2, succ u1} n m) [_inst_6 : Invertible.{max u1 u3} (Matrix.{u1, u1, u3} m m α) (Matrix.instMulMatrix.{u3, u1} m α _inst_4 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u1} m α (fun (a : m) (b : m) => _inst_5 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (Semiring.toOne.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) A] [_inst_7 : Invertible.{max u3 u2} (Matrix.{u2, u2, u3} n n α) (Matrix.instMulMatrix.{u3, u2} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (Semiring.toOne.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) (Matrix.submatrix.{u3, u2, u1, u1, u2} n m m n α A (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₁) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₂))], Eq.{max (succ u2) (succ u3)} (Matrix.{u2, u2, u3} n n α) (Invertible.invOf.{max u3 u2} (Matrix.{u2, u2, u3} n n α) (Matrix.instMulMatrix.{u3, u2} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (Semiring.toOne.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) (Matrix.submatrix.{u3, u2, u1, u1, u2} n m m n α A (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₁) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₂)) _inst_7) (Matrix.submatrix.{u3, u2, u1, u1, u2} n m m n α (Invertible.invOf.{max u1 u3} (Matrix.{u1, u1, u3} m m α) (Matrix.instMulMatrix.{u3, u1} m α _inst_4 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u1} m α (fun (a : m) (b : m) => _inst_5 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (Semiring.toOne.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) A _inst_6) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₂) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₁))
 Case conversion may be inaccurate. Consider using '#align matrix.inv_of_submatrix_equiv_eq Matrix.invOf_submatrix_equiv_eqₓ'. -/
 theorem invOf_submatrix_equiv_eq (A : Matrix m m α) (e₁ e₂ : n ≃ m) [Invertible A]
     [Invertible (A.submatrix e₁ e₂)] : ⅟ (A.submatrix e₁ e₂) = (⅟ A).submatrix e₂ e₁ :=
@@ -1204,7 +1204,7 @@ theorem invOf_submatrix_equiv_eq (A : Matrix m m α) (e₁ e₂ : n ≃ m) [Inve
 lean 3 declaration is
   forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] [_inst_4 : Fintype.{u1} m] [_inst_5 : DecidableEq.{succ u1} m] (A : Matrix.{u1, u1, u3} m m α) (e₁ : Equiv.{succ u2, succ u1} n m) (e₂ : Equiv.{succ u2, succ u1} n m), Equiv.{succ (max u2 u3), succ (max u1 u3)} (Invertible.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.hasMul.{u3, u2} n α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.hasOne.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u3} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (AddMonoidWithOne.toOne.{u3} α (AddGroupWithOne.toAddMonoidWithOne.{u3} α (AddCommGroupWithOne.toAddGroupWithOne.{u3} α (Ring.toAddCommGroupWithOne.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.submatrix.{u3, u2, u1, u1, u2} n m m n α A (coeFn.{max 1 (max (succ u2) (succ u1)) (succ u1) (succ u2), max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} n m) (fun (_x : Equiv.{succ u2, succ u1} n m) => n -> m) (Equiv.hasCoeToFun.{succ u2, succ u1} n m) e₁) (coeFn.{max 1 (max (succ u2) (succ u1)) (succ u1) (succ u2), max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} n m) (fun (_x : Equiv.{succ u2, succ u1} n m) => n -> m) (Equiv.hasCoeToFun.{succ u2, succ u1} n m) e₂))) (Invertible.{max u1 u3} (Matrix.{u1, u1, u3} m m α) (Matrix.hasMul.{u3, u1} m α _inst_4 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.hasOne.{u3, u1} m α (fun (a : m) (b : m) => _inst_5 a b) (MulZeroClass.toHasZero.{u3} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (AddMonoidWithOne.toOne.{u3} α (AddGroupWithOne.toAddMonoidWithOne.{u3} α (AddCommGroupWithOne.toAddGroupWithOne.{u3} α (Ring.toAddCommGroupWithOne.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) A)
 but is expected to have type
-  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] [_inst_4 : Fintype.{u1} m] [_inst_5 : DecidableEq.{succ u1} m] (A : Matrix.{u1, u1, u3} m m α) (e₁ : Equiv.{succ u2, succ u1} n m) (e₂ : Equiv.{succ u2, succ u1} n m), Equiv.{succ (max u3 u2), succ (max u1 u3)} (Invertible.{max u3 u2} (Matrix.{u2, u2, u3} n n α) (Matrix.instMulMatrix.{u3, u2} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (NonAssocRing.toOne.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (Matrix.submatrix.{u3, u2, u1, u1, u2} n m m n α A (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₁) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₂))) (Invertible.{max u1 u3} (Matrix.{u1, u1, u3} m m α) (Matrix.instMulMatrix.{u3, u1} m α _inst_4 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u1} m α (fun (a : m) (b : m) => _inst_5 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (NonAssocRing.toOne.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) A)
+  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] [_inst_4 : Fintype.{u1} m] [_inst_5 : DecidableEq.{succ u1} m] (A : Matrix.{u1, u1, u3} m m α) (e₁ : Equiv.{succ u2, succ u1} n m) (e₂ : Equiv.{succ u2, succ u1} n m), Equiv.{succ (max u3 u2), succ (max u1 u3)} (Invertible.{max u3 u2} (Matrix.{u2, u2, u3} n n α) (Matrix.instMulMatrix.{u3, u2} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (Semiring.toOne.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) (Matrix.submatrix.{u3, u2, u1, u1, u2} n m m n α A (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₁) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e₂))) (Invertible.{max u1 u3} (Matrix.{u1, u1, u3} m m α) (Matrix.instMulMatrix.{u3, u1} m α _inst_4 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u1} m α (fun (a : m) (b : m) => _inst_5 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (Semiring.toOne.{u3} α (CommSemiring.toSemiring.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3)))) A)
 Case conversion may be inaccurate. Consider using '#align matrix.submatrix_equiv_invertible_equiv_invertible Matrix.submatrixEquivInvertibleEquivInvertibleₓ'. -/
 /-- Together `matrix.submatrix_equiv_invertible` and
 `matrix.invertible_of_submatrix_equiv_invertible` form an equivalence, although both sides of the
@@ -1271,7 +1271,7 @@ variable [Fintype m] [DecidableEq m]
 lean 3 declaration is
   forall {m : Type.{u1}} {α : Type.{u2}} [_inst_3 : CommRing.{u2} α] [_inst_4 : Fintype.{u1} m] [_inst_5 : DecidableEq.{succ u1} m] {M : Matrix.{u1, u1, u2} m m α}, (IsUnit.{max u1 u2} (Matrix.{u1, u1, u2} m m α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} m m α) (Matrix.ring.{u2, u1} m α _inst_4 (fun (a : m) (b : m) => _inst_5 a b) (CommRing.toRing.{u2} α _inst_3))) M) -> (forall (N : Matrix.{u1, u1, u2} m m α), Eq.{succ u2} α (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_5 a b) _inst_4 α _inst_3 (Matrix.mul.{u2, u1, u1, u1} m m m α _inst_4 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.mul.{u2, u1, u1, u1} m m m α _inst_4 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) M N) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} m m α) (Matrix.hasInv.{u1, u2} m α _inst_4 (fun (a : m) (b : m) => _inst_5 a b) _inst_3) M))) (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_5 a b) _inst_4 α _inst_3 N))
 but is expected to have type
-  forall {m : Type.{u1}} {α : Type.{u2}} [_inst_3 : CommRing.{u2} α] [_inst_4 : Fintype.{u1} m] [_inst_5 : DecidableEq.{succ u1} m] {M : Matrix.{u1, u1, u2} m m α}, (IsUnit.{max u1 u2} (Matrix.{u1, u1, u2} m m α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} m m α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} m m α) (Matrix.semiring.{u2, u1} m α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) _inst_4 (fun (a : m) (b : m) => _inst_5 a b)))) M) -> (forall (N : Matrix.{u1, u1, u2} m m α), Eq.{succ u2} α (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_5 a b) _inst_4 α _inst_3 (Matrix.mul.{u2, u1, u1, u1} m m m α _inst_4 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.mul.{u2, u1, u1, u1} m m m α _inst_4 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) M N) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} m m α) (Matrix.inv.{u1, u2} m α _inst_4 (fun (a : m) (b : m) => _inst_5 a b) _inst_3) M))) (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_5 a b) _inst_4 α _inst_3 N))
+  forall {m : Type.{u1}} {α : Type.{u2}} [_inst_3 : CommRing.{u2} α] [_inst_4 : Fintype.{u1} m] [_inst_5 : DecidableEq.{succ u1} m] {M : Matrix.{u1, u1, u2} m m α}, (IsUnit.{max u1 u2} (Matrix.{u1, u1, u2} m m α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} m m α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} m m α) (Matrix.semiring.{u2, u1} m α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_4 (fun (a : m) (b : m) => _inst_5 a b)))) M) -> (forall (N : Matrix.{u1, u1, u2} m m α), Eq.{succ u2} α (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_5 a b) _inst_4 α _inst_3 (Matrix.mul.{u2, u1, u1, u1} m m m α _inst_4 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.mul.{u2, u1, u1, u1} m m m α _inst_4 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) M N) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} m m α) (Matrix.inv.{u1, u2} m α _inst_4 (fun (a : m) (b : m) => _inst_5 a b) _inst_3) M))) (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_5 a b) _inst_4 α _inst_3 N))
 Case conversion may be inaccurate. Consider using '#align matrix.det_conj Matrix.det_conjₓ'. -/
 /-- A variant of `matrix.det_units_conj`. -/
 theorem det_conj {M : Matrix m m α} (h : IsUnit M) (N : Matrix m m α) : det (M ⬝ N ⬝ M⁻¹) = det N :=
@@ -1282,7 +1282,7 @@ theorem det_conj {M : Matrix m m α} (h : IsUnit M) (N : Matrix m m α) : det (M
 lean 3 declaration is
   forall {m : Type.{u1}} {α : Type.{u2}} [_inst_3 : CommRing.{u2} α] [_inst_4 : Fintype.{u1} m] [_inst_5 : DecidableEq.{succ u1} m] {M : Matrix.{u1, u1, u2} m m α}, (IsUnit.{max u1 u2} (Matrix.{u1, u1, u2} m m α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} m m α) (Matrix.ring.{u2, u1} m α _inst_4 (fun (a : m) (b : m) => _inst_5 a b) (CommRing.toRing.{u2} α _inst_3))) M) -> (forall (N : Matrix.{u1, u1, u2} m m α), Eq.{succ u2} α (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_5 a b) _inst_4 α _inst_3 (Matrix.mul.{u2, u1, u1, u1} m m m α _inst_4 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.mul.{u2, u1, u1, u1} m m m α _inst_4 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} m m α) (Matrix.hasInv.{u1, u2} m α _inst_4 (fun (a : m) (b : m) => _inst_5 a b) _inst_3) M) N) M)) (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_5 a b) _inst_4 α _inst_3 N))
 but is expected to have type
-  forall {m : Type.{u1}} {α : Type.{u2}} [_inst_3 : CommRing.{u2} α] [_inst_4 : Fintype.{u1} m] [_inst_5 : DecidableEq.{succ u1} m] {M : Matrix.{u1, u1, u2} m m α}, (IsUnit.{max u1 u2} (Matrix.{u1, u1, u2} m m α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} m m α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} m m α) (Matrix.semiring.{u2, u1} m α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) _inst_4 (fun (a : m) (b : m) => _inst_5 a b)))) M) -> (forall (N : Matrix.{u1, u1, u2} m m α), Eq.{succ u2} α (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_5 a b) _inst_4 α _inst_3 (Matrix.mul.{u2, u1, u1, u1} m m m α _inst_4 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.mul.{u2, u1, u1, u1} m m m α _inst_4 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} m m α) (Matrix.inv.{u1, u2} m α _inst_4 (fun (a : m) (b : m) => _inst_5 a b) _inst_3) M) N) M)) (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_5 a b) _inst_4 α _inst_3 N))
+  forall {m : Type.{u1}} {α : Type.{u2}} [_inst_3 : CommRing.{u2} α] [_inst_4 : Fintype.{u1} m] [_inst_5 : DecidableEq.{succ u1} m] {M : Matrix.{u1, u1, u2} m m α}, (IsUnit.{max u1 u2} (Matrix.{u1, u1, u2} m m α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} m m α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} m m α) (Matrix.semiring.{u2, u1} m α (CommSemiring.toSemiring.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)) _inst_4 (fun (a : m) (b : m) => _inst_5 a b)))) M) -> (forall (N : Matrix.{u1, u1, u2} m m α), Eq.{succ u2} α (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_5 a b) _inst_4 α _inst_3 (Matrix.mul.{u2, u1, u1, u1} m m m α _inst_4 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.mul.{u2, u1, u1, u1} m m m α _inst_4 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} m m α) (Matrix.inv.{u1, u2} m α _inst_4 (fun (a : m) (b : m) => _inst_5 a b) _inst_3) M) N) M)) (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_5 a b) _inst_4 α _inst_3 N))
 Case conversion may be inaccurate. Consider using '#align matrix.det_conj' Matrix.det_conj'ₓ'. -/
 /-- A variant of `matrix.det_units_conj'`. -/
 theorem det_conj' {M : Matrix m m α} (h : IsUnit M) (N : Matrix m m α) :

mathlib commit https://github.com/leanprover-community/mathlib/commit/36b8aa61ea7c05727161f96a0532897bd72aedab

@@ -1118,7 +1118,7 @@ theorem list_prod_inv_reverse : ∀ l : List (Matrix n n α), l.Prod⁻¹ = (l.r
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (b : n -> α), (IsUnit.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{succ (max u1 u2)} (n -> α) (SMul.smul.{u2, max u1 u2} α (n -> α) (Function.hasSMul.{u1, u2, u2} n α α (Mul.toSMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) (Matrix.mulVec.{u2, u1, u1} n n α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) _inst_1 (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) b)) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u2, u2, max u1 u2, max u1 u2} α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (n -> α) (n -> α) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.Function.module.{u1, u2, u2} n α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Pi.Function.module.{u1, u2, u2} n α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (_x : LinearMap.{u2, u2, max u1 u2, max u1 u2} α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (n -> α) (n -> α) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.Function.module.{u1, u2, u2} n α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Pi.Function.module.{u1, u2, u2} n α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) => (n -> α) -> n -> α) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, max u1 u2} α α (n -> α) (n -> α) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.Function.module.{u1, u2, u2} n α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Pi.Function.module.{u1, u2, u2} n α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.cramer.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 A) b))
 but is expected to have type
-  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (b : n -> α), (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{max (succ u1) (succ u2)} (n -> α) (HSMul.hSMul.{u2, max u1 u2, max u1 u2} α (n -> α) (n -> α) (instHSMul.{u2, max u1 u2} α (n -> α) (Pi.instSMul.{u1, u2, u2} n α (fun (a._@.Mathlib.Data.Matrix.Basic._hyg.18076 : n) => α) (fun (i : n) => Algebra.toSMul.{u2, u2} α α (CommRing.toCommSemiring.{u2} α _inst_3) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Algebra.id.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) (Matrix.mulVec.{u2, u1, u1} n n α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) _inst_1 (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) b)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u2, u2, max u1 u2, max u1 u2} α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (RingHom.id.{u2} α (NonAssocRing.toNonAssocSemiring.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (n -> α) (n -> α) (Pi.addCommMonoid.{u1, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (n -> α) (fun (_x : n -> α) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : n -> α) => n -> α) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, max u1 u2} α α (n -> α) (n -> α) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (RingHom.id.{u2} α (NonAssocRing.toNonAssocSemiring.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.cramer.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 A) b))
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (b : n -> α), (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{max (succ u1) (succ u2)} (n -> α) (HSMul.hSMul.{u2, max u1 u2, max u1 u2} α (n -> α) (n -> α) (instHSMul.{u2, max u1 u2} α (n -> α) (Pi.instSMul.{u1, u2, u2} n α (fun (a._@.Mathlib.Data.Matrix.Basic._hyg.18074 : n) => α) (fun (i : n) => Algebra.toSMul.{u2, u2} α α (CommRing.toCommSemiring.{u2} α _inst_3) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Algebra.id.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) (Matrix.mulVec.{u2, u1, u1} n n α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) _inst_1 (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) b)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u2, u2, max u1 u2, max u1 u2} α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (RingHom.id.{u2} α (NonAssocRing.toNonAssocSemiring.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (n -> α) (n -> α) (Pi.addCommMonoid.{u1, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (n -> α) (fun (_x : n -> α) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : n -> α) => n -> α) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, max u1 u2} α α (n -> α) (n -> α) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (RingHom.id.{u2} α (NonAssocRing.toNonAssocSemiring.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.cramer.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 A) b))
 Case conversion may be inaccurate. Consider using '#align matrix.det_smul_inv_mul_vec_eq_cramer Matrix.det_smul_inv_mulVec_eq_cramerₓ'. -/
 /-- One form of **Cramer's rule**. See `matrix.mul_vec_cramer` for a stronger form. -/
 @[simp]
@@ -1132,7 +1132,7 @@ theorem det_smul_inv_mulVec_eq_cramer (A : Matrix n n α) (b : n → α) (h : Is
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (b : n -> α), (IsUnit.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{succ (max u1 u2)} (n -> α) (SMul.smul.{u2, max u1 u2} α (n -> α) (Function.hasSMul.{u1, u2, u2} n α α (Mul.toSMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) (Matrix.vecMul.{u2, u1, u1} n n α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) _inst_1 b (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A))) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (LinearMap.{u2, u2, max u1 u2, max u1 u2} α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (n -> α) (n -> α) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.Function.module.{u1, u2, u2} n α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} α 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α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) => (n -> α) -> n -> α) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, max u1 u2} α α (n -> α) (n -> α) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.Function.module.{u1, u2, u2} n α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Pi.Function.module.{u1, u2, u2} n α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.cramer.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 (Matrix.transpose.{u2, u1, u1} n n α A)) b))
 but is expected to have type
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(CommRing.toRing.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (n -> α) (fun (_x : n -> α) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : n -> α) => n -> α) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, max u1 u2} α α (n -> α) (n -> α) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (RingHom.id.{u2} α (NonAssocRing.toNonAssocSemiring.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.cramer.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 (Matrix.transpose.{u2, u1, u1} n n α A)) b))
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (b : n -> α), (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{max (succ u1) (succ u2)} (n -> α) (HSMul.hSMul.{u2, max u1 u2, max u1 u2} α (n -> α) (n -> α) (instHSMul.{u2, max u1 u2} α (n -> α) (Pi.instSMul.{u1, u2, u2} n α (fun (a._@.Mathlib.Data.Matrix.Basic._hyg.18132 : n) => α) (fun (i : n) => Algebra.toSMul.{u2, u2} α α (CommRing.toCommSemiring.{u2} α _inst_3) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Algebra.id.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) (Matrix.vecMul.{u2, u1, u1} n n α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) _inst_1 b (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u2, u2, max u1 u2, max u1 u2} α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (RingHom.id.{u2} α (NonAssocRing.toNonAssocSemiring.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (n -> α) (n -> α) (Pi.addCommMonoid.{u1, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (n -> α) (fun (_x : n -> α) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : n -> α) => n -> α) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, max u1 u2} α α (n -> α) (n -> α) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (RingHom.id.{u2} α (NonAssocRing.toNonAssocSemiring.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.cramer.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 (Matrix.transpose.{u2, u1, u1} n n α A)) b))
 Case conversion may be inaccurate. Consider using '#align matrix.det_smul_inv_vec_mul_eq_cramer_transpose Matrix.det_smul_inv_vecMul_eq_cramer_transposeₓ'. -/
 /-- One form of **Cramer's rule**. See `matrix.mul_vec_cramer` for a stronger form. -/
 @[simp]

mathlib commit https://github.com/leanprover-community/mathlib/commit/fa78268d4d77cb2b2fbc89f0527e2e7807763780

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Tim Baanen, Lu-Ming Zhang
 
 ! This file was ported from Lean 3 source module linear_algebra.matrix.nonsingular_inverse
-! leanprover-community/mathlib commit a07a7ae98384cd6485d7825e161e528ba78ef3bc
+! leanprover-community/mathlib commit 9d2f0748e6c50d7a2657c564b1ff2c695b39148d
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.LinearAlgebra.Matrix.Adjugate
 /-!
 # Nonsingular inverses
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file, we define an inverse for square matrices of invertible determinant.
 
 For matrices that are not square or not of full rank, there is a more general notion of

mathlib commit https://github.com/leanprover-community/mathlib/commit/9b2b58d6b14b895b2f375108e765cb47de71aebd

@@ -1115,7 +1115,7 @@ theorem list_prod_inv_reverse : ∀ l : List (Matrix n n α), l.Prod⁻¹ = (l.r
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (b : n -> α), (IsUnit.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{succ (max u1 u2)} (n -> α) (SMul.smul.{u2, max u1 u2} α (n -> α) (Function.hasSMul.{u1, u2, u2} n α α (Mul.toSMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) (Matrix.mulVec.{u2, u1, u1} n n α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) _inst_1 (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) b)) (coeFn.{succ (max u1 u2), 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α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) => (n -> α) -> n -> α) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, max u1 u2} α α (n -> α) (n -> α) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.Function.module.{u1, u2, u2} n α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Pi.Function.module.{u1, u2, u2} n α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.cramer.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 A) b))
 but is expected to have type
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(CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => _private.Mathlib.RingTheory.Ideal.Operations.0.Ideal.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRing.{u2, u2} α α (CommRing.toCommSemiring.{u2} α _inst_3) _inst_3 (Algebra.id.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => _private.Mathlib.RingTheory.Ideal.Operations.0.Ideal.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRing.{u2, u2} α α (CommRing.toCommSemiring.{u2} α _inst_3) _inst_3 (Algebra.id.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (n -> α) (fun (_x : n -> α) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : n -> α) => n -> α) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, max u1 u2} α α (n -> α) (n -> α) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => _private.Mathlib.RingTheory.Ideal.Operations.0.Ideal.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRing.{u2, u2} α α (CommRing.toCommSemiring.{u2} α _inst_3) _inst_3 (Algebra.id.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => _private.Mathlib.RingTheory.Ideal.Operations.0.Ideal.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRing.{u2, u2} α α (CommRing.toCommSemiring.{u2} α _inst_3) _inst_3 (Algebra.id.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (RingHom.id.{u2} α (NonAssocRing.toNonAssocSemiring.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.cramer.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 A) b))
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (b : n -> α), (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{max (succ u1) (succ u2)} (n -> α) (HSMul.hSMul.{u2, max u1 u2, max u1 u2} α (n -> α) (n -> α) (instHSMul.{u2, max u1 u2} α (n -> α) (Pi.instSMul.{u1, u2, u2} n α (fun (a._@.Mathlib.Data.Matrix.Basic._hyg.18076 : n) => α) (fun (i : n) => Algebra.toSMul.{u2, u2} α α (CommRing.toCommSemiring.{u2} α _inst_3) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Algebra.id.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) (Matrix.mulVec.{u2, u1, u1} n n α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) _inst_1 (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) b)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u2, u2, max u1 u2, max u1 u2} α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (RingHom.id.{u2} α (NonAssocRing.toNonAssocSemiring.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (n -> α) (n -> α) (Pi.addCommMonoid.{u1, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (n -> α) (fun (_x : n -> α) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : n -> α) => n -> α) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, max u1 u2} α α (n -> α) (n -> α) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (RingHom.id.{u2} α (NonAssocRing.toNonAssocSemiring.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.cramer.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 A) b))
 Case conversion may be inaccurate. Consider using '#align matrix.det_smul_inv_mul_vec_eq_cramer Matrix.det_smul_inv_mulVec_eq_cramerₓ'. -/
 /-- One form of **Cramer's rule**. See `matrix.mul_vec_cramer` for a stronger form. -/
 @[simp]
@@ -1129,7 +1129,7 @@ theorem det_smul_inv_mulVec_eq_cramer (A : Matrix n n α) (b : n → α) (h : Is
 lean 3 declaration is
   forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (b : n -> α), (IsUnit.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{succ (max u1 u2)} (n -> α) (SMul.smul.{u2, max u1 u2} α (n -> α) (Function.hasSMul.{u1, u2, u2} n α α (Mul.toSMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) (Matrix.vecMul.{u2, u1, u1} n n α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) _inst_1 b (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A))) (coeFn.{succ (max u1 u2), 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(NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Pi.Function.module.{u1, u2, u2} n α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (_x : LinearMap.{u2, u2, max u1 u2, max u1 u2} α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (n -> α) (n -> α) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.Function.module.{u1, u2, u2} n α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Pi.Function.module.{u1, u2, u2} n α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) => (n -> α) -> n -> α) (LinearMap.hasCoeToFun.{u2, u2, max u1 u2, max u1 u2} α α (n -> α) (n -> α) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.Function.module.{u1, u2, u2} n α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Pi.Function.module.{u1, u2, u2} n α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (RingHom.id.{u2} α (Semiring.toNonAssocSemiring.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.cramer.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 (Matrix.transpose.{u2, u1, u1} n n α A)) b))
 but is expected to have type
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(NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) _inst_1 b (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u2, u2, max u1 u2, max u1 u2} α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (RingHom.id.{u2} α (NonAssocRing.toNonAssocSemiring.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (n -> α) (n -> α) (Pi.addCommMonoid.{u1, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => _private.Mathlib.RingTheory.Ideal.Operations.0.Ideal.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRing.{u2, u2} α α (CommRing.toCommSemiring.{u2} α _inst_3) _inst_3 (Algebra.id.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => _private.Mathlib.RingTheory.Ideal.Operations.0.Ideal.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRing.{u2, u2} α α (CommRing.toCommSemiring.{u2} α _inst_3) _inst_3 (Algebra.id.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (n -> α) (fun (_x : n -> α) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : n -> α) => n -> α) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, max u1 u2} α α (n -> α) (n -> α) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => _private.Mathlib.RingTheory.Ideal.Operations.0.Ideal.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRing.{u2, u2} α α (CommRing.toCommSemiring.{u2} α _inst_3) _inst_3 (Algebra.id.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => _private.Mathlib.RingTheory.Ideal.Operations.0.Ideal.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRing.{u2, u2} α α (CommRing.toCommSemiring.{u2} α _inst_3) _inst_3 (Algebra.id.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (RingHom.id.{u2} α (NonAssocRing.toNonAssocSemiring.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.cramer.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 (Matrix.transpose.{u2, u1, u1} n n α A)) b))
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (b : n -> α), (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{max (succ u1) (succ u2)} (n -> α) (HSMul.hSMul.{u2, max u1 u2, max u1 u2} α (n -> α) (n -> α) (instHSMul.{u2, max u1 u2} α (n -> α) (Pi.instSMul.{u1, u2, u2} n α (fun (a._@.Mathlib.Data.Matrix.Basic._hyg.18134 : n) => α) (fun (i : n) => Algebra.toSMul.{u2, u2} α α (CommRing.toCommSemiring.{u2} α _inst_3) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Algebra.id.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) (Matrix.vecMul.{u2, u1, u1} n n α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) _inst_1 b (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u2, u2, max u1 u2, max u1 u2} α α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (RingHom.id.{u2} α (NonAssocRing.toNonAssocSemiring.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (n -> α) (n -> α) (Pi.addCommMonoid.{u1, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (n -> α) (fun (_x : n -> α) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : n -> α) => n -> α) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u2, max u1 u2} α α (n -> α) (n -> α) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.addCommMonoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Pi.module.{u1, u2, u2} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.Adjugate._hyg.274 : n) => α) α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (fun (i : n) => Semiring.toModule.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (RingHom.id.{u2} α (NonAssocRing.toNonAssocSemiring.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.cramer.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 (Matrix.transpose.{u2, u1, u1} n n α A)) b))
 Case conversion may be inaccurate. Consider using '#align matrix.det_smul_inv_vec_mul_eq_cramer_transpose Matrix.det_smul_inv_vecMul_eq_cramer_transposeₓ'. -/
 /-- One form of **Cramer's rule**. See `matrix.mul_vec_cramer` for a stronger form. -/
 @[simp]

mathlib commit https://github.com/leanprover-community/mathlib/commit/2651125b48fc5c170ab1111afd0817c903b1fc6c

@@ -69,31 +69,67 @@ section Invertible
 
 variable [Fintype n] [DecidableEq n] [CommRing α]
 
+/- warning: matrix.inv_of_mul_self -> Matrix.invOf_mul_self is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align matrix.inv_of_mul_self Matrix.invOf_mul_selfₓ'. -/
 /-- A copy of `inv_of_mul_self` using `⬝` not `*`. -/
 protected theorem invOf_mul_self (A : Matrix n n α) [Invertible A] : ⅟ A ⬝ A = 1 :=
   invOf_mul_self A
 #align matrix.inv_of_mul_self Matrix.invOf_mul_self
 
+/- warning: matrix.mul_inv_of_self -> Matrix.mul_invOf_self is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align matrix.mul_inv_of_self Matrix.mul_invOf_selfₓ'. -/
 /-- A copy of `mul_inv_of_self` using `⬝` not `*`. -/
 protected theorem mul_invOf_self (A : Matrix n n α) [Invertible A] : A ⬝ ⅟ A = 1 :=
   mul_invOf_self A
 #align matrix.mul_inv_of_self Matrix.mul_invOf_self
 
+/- warning: matrix.inv_of_mul_self_assoc -> Matrix.invOf_mul_self_assoc is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align matrix.inv_of_mul_self_assoc Matrix.invOf_mul_self_assocₓ'. -/
 /-- A copy of `inv_of_mul_self_assoc` using `⬝` not `*`. -/
 protected theorem invOf_mul_self_assoc (A : Matrix n n α) (B : Matrix n m α) [Invertible A] :
     ⅟ A ⬝ (A ⬝ B) = B := by rw [← Matrix.mul_assoc, Matrix.invOf_mul_self, Matrix.one_mul]
 #align matrix.inv_of_mul_self_assoc Matrix.invOf_mul_self_assoc
 
+/- warning: matrix.mul_inv_of_self_assoc -> Matrix.mul_invOf_self_assoc is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align matrix.mul_inv_of_self_assoc Matrix.mul_invOf_self_assocₓ'. -/
 /-- A copy of `mul_inv_of_self_assoc` using `⬝` not `*`. -/
 protected theorem mul_invOf_self_assoc (A : Matrix n n α) (B : Matrix n m α) [Invertible A] :
     A ⬝ (⅟ A ⬝ B) = B := by rw [← Matrix.mul_assoc, Matrix.mul_invOf_self, Matrix.one_mul]
 #align matrix.mul_inv_of_self_assoc Matrix.mul_invOf_self_assoc
 
+/- warning: matrix.mul_inv_of_mul_self_cancel -> Matrix.mul_invOf_mul_self_cancel is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align matrix.mul_inv_of_mul_self_cancel Matrix.mul_invOf_mul_self_cancelₓ'. -/
 /-- A copy of `mul_inv_of_mul_self_cancel` using `⬝` not `*`. -/
 protected theorem mul_invOf_mul_self_cancel (A : Matrix m n α) (B : Matrix n n α) [Invertible B] :
     A ⬝ ⅟ B ⬝ B = A := by rw [Matrix.mul_assoc, Matrix.invOf_mul_self, Matrix.mul_one]
 #align matrix.mul_inv_of_mul_self_cancel Matrix.mul_invOf_mul_self_cancel
 
+/- warning: matrix.mul_mul_inv_of_self_cancel -> Matrix.mul_mul_invOf_self_cancel is a dubious translation:
+lean 3 declaration is
+  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] (A : Matrix.{u1, u2, u3} m n α) (B : Matrix.{u2, u2, u3} n n α) [_inst_4 : Invertible.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.hasMul.{u3, u2} n α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.hasOne.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u3} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (AddMonoidWithOne.toOne.{u3} α (AddGroupWithOne.toAddMonoidWithOne.{u3} α (AddCommGroupWithOne.toAddGroupWithOne.{u3} α (Ring.toAddCommGroupWithOne.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) B], Eq.{succ (max u1 u2 u3)} (Matrix.{u1, u2, u3} m n α) (Matrix.mul.{u3, u1, u2, u2} m n n α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) (Matrix.mul.{u3, u1, u2, u2} m n n α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) A B) (Invertible.invOf.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.hasMul.{u3, u2} n α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.hasOne.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u3} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (AddMonoidWithOne.toOne.{u3} α (AddGroupWithOne.toAddMonoidWithOne.{u3} α (AddCommGroupWithOne.toAddGroupWithOne.{u3} α (Ring.toAddCommGroupWithOne.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) B _inst_4)) A
+but is expected to have type
+  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] (A : Matrix.{u1, u2, u3} m n α) (B : Matrix.{u2, u2, u3} n n α) [_inst_4 : Invertible.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.instMulMatrix.{u3, u2} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (NonAssocRing.toOne.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) B], Eq.{max (max (succ u1) (succ u2)) (succ u3)} (Matrix.{u1, u2, u3} m n α) (Matrix.mul.{u3, u1, u2, u2} m n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) (Matrix.mul.{u3, u1, u2, u2} m n n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) A B) (Invertible.invOf.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.instMulMatrix.{u3, u2} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.one.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} α (CommSemiring.toCommMonoidWithZero.{u3} α (CommRing.toCommSemiring.{u3} α _inst_3))) (NonAssocRing.toOne.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))) B _inst_4)) A
+Case conversion may be inaccurate. Consider using '#align matrix.mul_mul_inv_of_self_cancel Matrix.mul_mul_invOf_self_cancelₓ'. -/
 /-- A copy of `mul_mul_inv_of_self_cancel` using `⬝` not `*`. -/
 protected theorem mul_mul_invOf_self_cancel (A : Matrix m n α) (B : Matrix n n α) [Invertible B] :
     A ⬝ B ⬝ ⅟ B = A := by rw [Matrix.mul_assoc, Matrix.mul_invOf_self, Matrix.mul_one]
@@ -101,6 +137,12 @@ protected theorem mul_mul_invOf_self_cancel (A : Matrix m n α) (B : Matrix n n
 
 variable (A : Matrix n n α) (B : Matrix n n α)
 
+/- warning: matrix.invertible_of_det_invertible -> Matrix.invertibleOfDetInvertible is a dubious translation:
+lean 3 declaration is
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)], Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) A
+but is expected to have type
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{u2} α (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)], Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) A
+Case conversion may be inaccurate. Consider using '#align matrix.invertible_of_det_invertible Matrix.invertibleOfDetInvertibleₓ'. -/
 /-- If `A.det` has a constructive inverse, produce one for `A`. -/
 def invertibleOfDetInvertible [Invertible A.det] : Invertible A
     where
@@ -111,12 +153,24 @@ def invertibleOfDetInvertible [Invertible A.det] : Invertible A
     rw [smul_mul_assoc, Matrix.mul_eq_mul, adjugate_mul, smul_smul, invOf_mul_self, one_smul]
 #align matrix.invertible_of_det_invertible Matrix.invertibleOfDetInvertible
 
+/- warning: matrix.inv_of_eq -> Matrix.invOf_eq is a dubious translation:
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+but is expected to have type
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{u2} α (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)] [_inst_5 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) A], Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Invertible.invOf.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) A _inst_5) (HSMul.hSMul.{u2, max u1 u2, max u1 u2} α (Matrix.{u1, u1, u2} n n α) (Matrix.{u1, u1, u2} n n α) (instHSMul.{u2, max u1 u2} α (Matrix.{u1, u1, u2} n n α) (Matrix.smul.{u2, u1, u1, u2} n n α α (Algebra.toSMul.{u2, u2} α α (CommRing.toCommSemiring.{u2} α _inst_3) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Algebra.id.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))))) (Invertible.invOf.{u2} α (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) _inst_4) (Matrix.adjugate.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 A))
+Case conversion may be inaccurate. Consider using '#align matrix.inv_of_eq Matrix.invOf_eqₓ'. -/
 theorem invOf_eq [Invertible A.det] [Invertible A] : ⅟ A = ⅟ A.det • A.adjugate :=
   by
   letI := invertible_of_det_invertible A
   convert(rfl : ⅟ A = _)
 #align matrix.inv_of_eq Matrix.invOf_eq
 
+/- warning: matrix.det_invertible_of_left_inverse -> Matrix.detInvertibleOfLeftInverse is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align matrix.det_invertible_of_left_inverse Matrix.detInvertibleOfLeftInverseₓ'. -/
 /-- `A.det` is invertible if `A` has a left inverse. -/
 def detInvertibleOfLeftInverse (h : B ⬝ A = 1) : Invertible A.det
     where
@@ -125,6 +179,12 @@ def detInvertibleOfLeftInverse (h : B ⬝ A = 1) : Invertible A.det
   invOf_mul_self := by rw [← det_mul, h, det_one]
 #align matrix.det_invertible_of_left_inverse Matrix.detInvertibleOfLeftInverse
 
+/- warning: matrix.det_invertible_of_right_inverse -> Matrix.detInvertibleOfRightInverse is a dubious translation:
+lean 3 declaration is
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (B : Matrix.{u1, u1, u2} n n α), (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A B) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n n α) 1 (One.one.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))))))) -> (Invertible.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align matrix.det_invertible_of_right_inverse Matrix.detInvertibleOfRightInverseₓ'. -/
 /-- `A.det` is invertible if `A` has a right inverse. -/
 def detInvertibleOfRightInverse (h : A ⬝ B = 1) : Invertible A.det
     where
@@ -133,17 +193,35 @@ def detInvertibleOfRightInverse (h : A ⬝ B = 1) : Invertible A.det
   invOf_mul_self := by rw [mul_comm, ← det_mul, h, det_one]
 #align matrix.det_invertible_of_right_inverse Matrix.detInvertibleOfRightInverse
 
+/- warning: matrix.det_invertible_of_invertible -> Matrix.detInvertibleOfInvertible is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align matrix.det_invertible_of_invertible Matrix.detInvertibleOfInvertibleₓ'. -/
 /-- If `A` has a constructive inverse, produce one for `A.det`. -/
 def detInvertibleOfInvertible [Invertible A] : Invertible A.det :=
   detInvertibleOfLeftInverse A (⅟ A) (invOf_mul_self _)
 #align matrix.det_invertible_of_invertible Matrix.detInvertibleOfInvertible
 
+/- warning: matrix.det_inv_of -> Matrix.det_invOf is a dubious translation:
+lean 3 declaration is
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) A] [_inst_5 : Invertible.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)], Eq.{succ u2} α (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 (Invertible.invOf.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) A _inst_4)) (Invertible.invOf.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) _inst_5)
+but is expected to have type
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) A] [_inst_5 : Invertible.{u2} α (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)], Eq.{succ u2} α (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 (Invertible.invOf.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) A _inst_4)) (Invertible.invOf.{u2} α (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) _inst_5)
+Case conversion may be inaccurate. Consider using '#align matrix.det_inv_of Matrix.det_invOfₓ'. -/
 theorem det_invOf [Invertible A] [Invertible A.det] : (⅟ A).det = ⅟ A.det :=
   by
   letI := det_invertible_of_invertible A
   convert(rfl : _ = ⅟ A.det)
 #align matrix.det_inv_of Matrix.det_invOf
 
+/- warning: matrix.invertible_equiv_det_invertible -> Matrix.invertibleEquivDetInvertible is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align matrix.invertible_equiv_det_invertible Matrix.invertibleEquivDetInvertibleₓ'. -/
 /-- Together `matrix.det_invertible_of_invertible` and `matrix.invertible_of_det_invertible` form an
 equivalence, although both sides of the equiv are subsingleton anyway. -/
 @[simps]
@@ -157,6 +235,12 @@ def invertibleEquivDetInvertible : Invertible A ≃ Invertible A.det
 
 variable {A B}
 
+/- warning: matrix.mul_eq_one_comm -> Matrix.mul_eq_one_comm is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.mul_eq_one_comm Matrix.mul_eq_one_commₓ'. -/
 theorem mul_eq_one_comm : A ⬝ B = 1 ↔ B ⬝ A = 1 :=
   suffices ∀ A B, A ⬝ B = 1 → B ⬝ A = 1 from ⟨this A B, this B A⟩
   fun A B h => by
@@ -172,22 +256,46 @@ theorem mul_eq_one_comm : A ⬝ B = 1 ↔ B ⬝ A = 1 :=
 
 variable (A B)
 
+/- warning: matrix.invertible_of_left_inverse -> Matrix.invertibleOfLeftInverse is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.invertible_of_left_inverse Matrix.invertibleOfLeftInverseₓ'. -/
 /-- We can construct an instance of invertible A if A has a left inverse. -/
 def invertibleOfLeftInverse (h : B ⬝ A = 1) : Invertible A :=
   ⟨B, h, mul_eq_one_comm.mp h⟩
 #align matrix.invertible_of_left_inverse Matrix.invertibleOfLeftInverse
 
+/- warning: matrix.invertible_of_right_inverse -> Matrix.invertibleOfRightInverse is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.invertible_of_right_inverse Matrix.invertibleOfRightInverseₓ'. -/
 /-- We can construct an instance of invertible A if A has a right inverse. -/
 def invertibleOfRightInverse (h : A ⬝ B = 1) : Invertible A :=
   ⟨B, mul_eq_one_comm.mp h, h⟩
 #align matrix.invertible_of_right_inverse Matrix.invertibleOfRightInverse
 
+/- warning: matrix.invertible_transpose -> Matrix.invertibleTranspose is a dubious translation:
+lean 3 declaration is
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) A], Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.transpose.{u2, u1, u1} n n α A)
+but is expected to have type
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) A], Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.transpose.{u2, u1, u1} n n α A)
+Case conversion may be inaccurate. Consider using '#align matrix.invertible_transpose Matrix.invertibleTransposeₓ'. -/
 /-- The transpose of an invertible matrix is invertible. -/
 instance invertibleTranspose [Invertible A] : Invertible Aᵀ :=
   haveI : Invertible Aᵀ.det := by simpa using det_invertible_of_invertible A
   invertible_of_det_invertible Aᵀ
 #align matrix.invertible_transpose Matrix.invertibleTranspose
 
+/- warning: matrix.invertible__of_invertible_transpose -> Matrix.invertibleOfInvertibleTranspose is a dubious translation:
+lean 3 declaration is
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.transpose.{u2, u1, u1} n n α A)], Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) A
+but is expected to have type
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.transpose.{u2, u1, u1} n n α A)], Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) A
+Case conversion may be inaccurate. Consider using '#align matrix.invertible__of_invertible_transpose Matrix.invertibleOfInvertibleTransposeₓ'. -/
 /-- A matrix is invertible if the transpose is invertible. -/
 def invertibleOfInvertibleTranspose [Invertible Aᵀ] : Invertible A :=
   by
@@ -195,6 +303,12 @@ def invertibleOfInvertibleTranspose [Invertible Aᵀ] : Invertible A :=
   infer_instance
 #align matrix.invertible__of_invertible_transpose Matrix.invertibleOfInvertibleTranspose
 
+/- warning: matrix.invertible_of_invertible_conj_transpose -> Matrix.invertibleOfInvertibleConjTranspose is a dubious translation:
+lean 3 declaration is
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : StarRing.{u2} α (NonUnitalRing.toNonUnitalSemiring.{u2} α (NonUnitalCommRing.toNonUnitalRing.{u2} α (CommRing.toNonUnitalCommRing.{u2} α _inst_3)))] [_inst_5 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.conjTranspose.{u2, u1, u1} n n α (InvolutiveStar.toHasStar.{u2} α (StarAddMonoid.toHasInvolutiveStar.{u2} α (AddCommMonoid.toAddMonoid.{u2} α (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} α (NonUnitalRing.toNonUnitalSemiring.{u2} α (NonUnitalCommRing.toNonUnitalRing.{u2} α (CommRing.toNonUnitalCommRing.{u2} α _inst_3)))))) (StarRing.toStarAddMonoid.{u2} α (NonUnitalRing.toNonUnitalSemiring.{u2} α (NonUnitalCommRing.toNonUnitalRing.{u2} α (CommRing.toNonUnitalCommRing.{u2} α _inst_3))) _inst_4))) A)], Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) A
+but is expected to have type
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : StarRing.{u2} α (NonUnitalRing.toNonUnitalSemiring.{u2} α (NonUnitalCommRing.toNonUnitalRing.{u2} α (CommRing.toNonUnitalCommRing.{u2} α _inst_3)))] [_inst_5 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.conjTranspose.{u2, u1, u1} n n α (InvolutiveStar.toStar.{u2} α (StarAddMonoid.toInvolutiveStar.{u2} α (AddMonoidWithOne.toAddMonoid.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (Ring.toAddGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (StarRing.toStarAddMonoid.{u2} α (NonUnitalRing.toNonUnitalSemiring.{u2} α (NonUnitalCommRing.toNonUnitalRing.{u2} α (CommRing.toNonUnitalCommRing.{u2} α _inst_3))) _inst_4))) A)], Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) A
+Case conversion may be inaccurate. Consider using '#align matrix.invertible_of_invertible_conj_transpose Matrix.invertibleOfInvertibleConjTransposeₓ'. -/
 /-- A matrix is invertible if the conjugate transpose is invertible. -/
 def invertibleOfInvertibleConjTranspose [StarRing α] [Invertible Aᴴ] : Invertible A :=
   by
@@ -202,11 +316,23 @@ def invertibleOfInvertibleConjTranspose [StarRing α] [Invertible Aᴴ] : Invert
   infer_instance
 #align matrix.invertible_of_invertible_conj_transpose Matrix.invertibleOfInvertibleConjTranspose
 
+/- warning: matrix.unit_of_det_invertible -> Matrix.unitOfDetInvertible is a dubious translation:
+lean 3 declaration is
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)], Units.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toRing.{u2} α _inst_3)))
+but is expected to have type
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{u2} α (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)], Units.{max u2 u1} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) _inst_1 (fun (a : n) (b : n) => _inst_2 a b))))
+Case conversion may be inaccurate. Consider using '#align matrix.unit_of_det_invertible Matrix.unitOfDetInvertibleₓ'. -/
 /-- Given a proof that `A.det` has a constructive inverse, lift `A` to `(matrix n n α)ˣ`-/
 def unitOfDetInvertible [Invertible A.det] : (Matrix n n α)ˣ :=
   @unitOfInvertible _ _ A (invertibleOfDetInvertible A)
 #align matrix.unit_of_det_invertible Matrix.unitOfDetInvertible
 
+/- warning: matrix.is_unit_iff_is_unit_det -> Matrix.isUnit_iff_isUnit_det is a dubious translation:
+lean 3 declaration is
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), Iff (IsUnit.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toRing.{u2} α _inst_3))) A) (IsUnit.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A))
+but is expected to have type
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α), Iff (IsUnit.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) _inst_1 (fun (a : n) (b : n) => _inst_2 a b)))) A) (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A))
+Case conversion may be inaccurate. Consider using '#align matrix.is_unit_iff_is_unit_det Matrix.isUnit_iff_isUnit_detₓ'. -/
 /-- When lowered to a prop, `matrix.invertible_equiv_det_invertible` forms an `iff`. -/
 theorem isUnit_iff_isUnit_det : IsUnit A ↔ IsUnit A.det := by
   simp only [← nonempty_invertible_iff_isUnit, (invertible_equiv_det_invertible A).nonempty_congr]
@@ -215,32 +341,74 @@ theorem isUnit_iff_isUnit_det : IsUnit A ↔ IsUnit A.det := by
 /-! #### Variants of the statements above with `is_unit`-/
 
 
+/- warning: matrix.is_unit_det_of_invertible -> Matrix.isUnit_det_of_invertible is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.is_unit_det_of_invertible Matrix.isUnit_det_of_invertibleₓ'. -/
 theorem isUnit_det_of_invertible [Invertible A] : IsUnit A.det :=
   @isUnit_of_invertible _ _ _ (detInvertibleOfInvertible A)
 #align matrix.is_unit_det_of_invertible Matrix.isUnit_det_of_invertible
 
 variable {A B}
 
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 theorem isUnit_of_left_inverse (h : B ⬝ A = 1) : IsUnit A :=
   ⟨⟨A, B, mul_eq_one_comm.mp h, h⟩, rfl⟩
 #align matrix.is_unit_of_left_inverse Matrix.isUnit_of_left_inverse
 
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 theorem isUnit_of_right_inverse (h : A ⬝ B = 1) : IsUnit A :=
   ⟨⟨A, B, h, mul_eq_one_comm.mp h⟩, rfl⟩
 #align matrix.is_unit_of_right_inverse Matrix.isUnit_of_right_inverse
 
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 theorem isUnit_det_of_left_inverse (h : B ⬝ A = 1) : IsUnit A.det :=
   @isUnit_of_invertible _ _ _ (detInvertibleOfLeftInverse _ _ h)
 #align matrix.is_unit_det_of_left_inverse Matrix.isUnit_det_of_left_inverse
 
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 theorem isUnit_det_of_right_inverse (h : A ⬝ B = 1) : IsUnit A.det :=
   @isUnit_of_invertible _ _ _ (detInvertibleOfRightInverse _ _ h)
 #align matrix.is_unit_det_of_right_inverse Matrix.isUnit_det_of_right_inverse
 
+/- warning: matrix.det_ne_zero_of_left_inverse -> Matrix.det_ne_zero_of_left_inverse is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.det_ne_zero_of_left_inverse Matrix.det_ne_zero_of_left_inverseₓ'. -/
 theorem det_ne_zero_of_left_inverse [Nontrivial α] (h : B ⬝ A = 1) : A.det ≠ 0 :=
   (isUnit_det_of_left_inverse h).NeZero
 #align matrix.det_ne_zero_of_left_inverse Matrix.det_ne_zero_of_left_inverse
 
+/- warning: matrix.det_ne_zero_of_right_inverse -> Matrix.det_ne_zero_of_right_inverse is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.det_ne_zero_of_right_inverse Matrix.det_ne_zero_of_right_inverseₓ'. -/
 theorem det_ne_zero_of_right_inverse [Nontrivial α] (h : A ⬝ B = 1) : A.det ≠ 0 :=
   (isUnit_det_of_right_inverse h).NeZero
 #align matrix.det_ne_zero_of_right_inverse Matrix.det_ne_zero_of_right_inverse
@@ -251,6 +419,12 @@ variable [Fintype n] [DecidableEq n] [CommRing α]
 
 variable (A : Matrix n n α) (B : Matrix n n α)
 
+/- warning: matrix.is_unit_det_transpose -> Matrix.isUnit_det_transpose is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.is_unit_det_transpose Matrix.isUnit_det_transposeₓ'. -/
 theorem isUnit_det_transpose (h : IsUnit A.det) : IsUnit Aᵀ.det :=
   by
   rw [det_transpose]
@@ -264,18 +438,42 @@ theorem isUnit_det_transpose (h : IsUnit A.det) : IsUnit Aᵀ.det :=
 noncomputable instance : Inv (Matrix n n α) :=
   ⟨fun A => Ring.inverse A.det • A.adjugate⟩
 
+/- warning: matrix.inv_def -> Matrix.inv_def is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.inv_def Matrix.inv_defₓ'. -/
 theorem inv_def (A : Matrix n n α) : A⁻¹ = Ring.inverse A.det • A.adjugate :=
   rfl
 #align matrix.inv_def Matrix.inv_def
 
+/- warning: matrix.nonsing_inv_apply_not_is_unit -> Matrix.nonsing_inv_apply_not_isUnit is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.nonsing_inv_apply_not_is_unit Matrix.nonsing_inv_apply_not_isUnitₓ'. -/
 theorem nonsing_inv_apply_not_isUnit (h : ¬IsUnit A.det) : A⁻¹ = 0 := by
   rw [inv_def, Ring.inverse_non_unit _ h, zero_smul]
 #align matrix.nonsing_inv_apply_not_is_unit Matrix.nonsing_inv_apply_not_isUnit
 
+/- warning: matrix.nonsing_inv_apply -> Matrix.nonsing_inv_apply is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.nonsing_inv_apply Matrix.nonsing_inv_applyₓ'. -/
 theorem nonsing_inv_apply (h : IsUnit A.det) : A⁻¹ = (↑h.Unit⁻¹ : α) • A.adjugate := by
   rw [inv_def, ← Ring.inverse_unit h.unit, IsUnit.unit_spec]
 #align matrix.nonsing_inv_apply Matrix.nonsing_inv_apply
 
+/- warning: matrix.inv_of_eq_nonsing_inv -> Matrix.invOf_eq_nonsing_inv is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.inv_of_eq_nonsing_inv Matrix.invOf_eq_nonsing_invₓ'. -/
 /-- The nonsingular inverse is the same as `inv_of` when `A` is invertible. -/
 @[simp]
 theorem invOf_eq_nonsing_inv [Invertible A] : ⅟ A = A⁻¹ :=
@@ -284,6 +482,12 @@ theorem invOf_eq_nonsing_inv [Invertible A] : ⅟ A = A⁻¹ :=
   rw [inv_def, Ring.inverse_invertible, inv_of_eq]
 #align matrix.inv_of_eq_nonsing_inv Matrix.invOf_eq_nonsing_inv
 
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+Case conversion may be inaccurate. Consider using '#align matrix.coe_units_inv Matrix.coe_units_invₓ'. -/
 /-- Coercing the result of `units.has_inv` is the same as coercing first and applying the
 nonsingular inverse. -/
 @[simp, norm_cast]
@@ -293,6 +497,12 @@ theorem coe_units_inv (A : (Matrix n n α)ˣ) : ↑A⁻¹ = (A⁻¹ : Matrix n n
   rw [← inv_of_eq_nonsing_inv, invOf_units]
 #align matrix.coe_units_inv Matrix.coe_units_inv
 
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+Case conversion may be inaccurate. Consider using '#align matrix.nonsing_inv_eq_ring_inverse Matrix.nonsing_inv_eq_ring_inverseₓ'. -/
 /-- The nonsingular inverse is the same as the general `ring.inverse`. -/
 theorem nonsing_inv_eq_ring_inverse : A⁻¹ = Ring.inverse A :=
   by
@@ -303,15 +513,33 @@ theorem nonsing_inv_eq_ring_inverse : A⁻¹ = Ring.inverse A :=
     rw [Ring.inverse_non_unit _ h, nonsing_inv_apply_not_is_unit A h_det]
 #align matrix.nonsing_inv_eq_ring_inverse Matrix.nonsing_inv_eq_ring_inverse
 
+/- warning: matrix.transpose_nonsing_inv -> Matrix.transpose_nonsing_inv is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.transpose_nonsing_inv Matrix.transpose_nonsing_invₓ'. -/
 theorem transpose_nonsing_inv : A⁻¹ᵀ = Aᵀ⁻¹ := by
   rw [inv_def, inv_def, transpose_smul, det_transpose, adjugate_transpose]
 #align matrix.transpose_nonsing_inv Matrix.transpose_nonsing_inv
 
+/- warning: matrix.conj_transpose_nonsing_inv -> Matrix.conjTranspose_nonsing_inv is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.conj_transpose_nonsing_inv Matrix.conjTranspose_nonsing_invₓ'. -/
 theorem conjTranspose_nonsing_inv [StarRing α] : A⁻¹ᴴ = Aᴴ⁻¹ := by
   rw [inv_def, inv_def, conj_transpose_smul, det_conj_transpose, adjugate_conj_transpose,
     Ring.inverse_star]
 #align matrix.conj_transpose_nonsing_inv Matrix.conjTranspose_nonsing_inv
 
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+Case conversion may be inaccurate. Consider using '#align matrix.mul_nonsing_inv Matrix.mul_nonsing_invₓ'. -/
 /-- The `nonsing_inv` of `A` is a right inverse. -/
 @[simp]
 theorem mul_nonsing_inv (h : IsUnit A.det) : A ⬝ A⁻¹ = 1 :=
@@ -320,6 +548,12 @@ theorem mul_nonsing_inv (h : IsUnit A.det) : A ⬝ A⁻¹ = 1 :=
   rw [← inv_of_eq_nonsing_inv, Matrix.mul_invOf_self]
 #align matrix.mul_nonsing_inv Matrix.mul_nonsing_inv
 
+/- warning: matrix.nonsing_inv_mul -> Matrix.nonsing_inv_mul is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.nonsing_inv_mul Matrix.nonsing_inv_mulₓ'. -/
 /-- The `nonsing_inv` of `A` is a left inverse. -/
 @[simp]
 theorem nonsing_inv_mul (h : IsUnit A.det) : A⁻¹ ⬝ A = 1 :=
@@ -333,73 +567,157 @@ instance [Invertible A] : Invertible A⁻¹ :=
   rw [← inv_of_eq_nonsing_inv]
   infer_instance
 
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+Case conversion may be inaccurate. Consider using '#align matrix.inv_inv_of_invertible Matrix.inv_inv_of_invertibleₓ'. -/
 @[simp]
 theorem inv_inv_of_invertible [Invertible A] : A⁻¹⁻¹ = A := by
   simp only [← inv_of_eq_nonsing_inv, invOf_invOf]
 #align matrix.inv_inv_of_invertible Matrix.inv_inv_of_invertible
 
+/- warning: matrix.mul_nonsing_inv_cancel_right -> Matrix.mul_nonsing_inv_cancel_right is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.mul_nonsing_inv_cancel_right Matrix.mul_nonsing_inv_cancel_rightₓ'. -/
 @[simp]
 theorem mul_nonsing_inv_cancel_right (B : Matrix m n α) (h : IsUnit A.det) : B ⬝ A ⬝ A⁻¹ = B := by
   simp [Matrix.mul_assoc, mul_nonsing_inv A h]
 #align matrix.mul_nonsing_inv_cancel_right Matrix.mul_nonsing_inv_cancel_right
 
+/- warning: matrix.mul_nonsing_inv_cancel_left -> Matrix.mul_nonsing_inv_cancel_left is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.mul_nonsing_inv_cancel_left Matrix.mul_nonsing_inv_cancel_leftₓ'. -/
 @[simp]
 theorem mul_nonsing_inv_cancel_left (B : Matrix n m α) (h : IsUnit A.det) : A ⬝ (A⁻¹ ⬝ B) = B := by
   simp [← Matrix.mul_assoc, mul_nonsing_inv A h]
 #align matrix.mul_nonsing_inv_cancel_left Matrix.mul_nonsing_inv_cancel_left
 
+/- warning: matrix.nonsing_inv_mul_cancel_right -> Matrix.nonsing_inv_mul_cancel_right is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.nonsing_inv_mul_cancel_right Matrix.nonsing_inv_mul_cancel_rightₓ'. -/
 @[simp]
 theorem nonsing_inv_mul_cancel_right (B : Matrix m n α) (h : IsUnit A.det) : B ⬝ A⁻¹ ⬝ A = B := by
   simp [Matrix.mul_assoc, nonsing_inv_mul A h]
 #align matrix.nonsing_inv_mul_cancel_right Matrix.nonsing_inv_mul_cancel_right
 
+/- warning: matrix.nonsing_inv_mul_cancel_left -> Matrix.nonsing_inv_mul_cancel_left is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.nonsing_inv_mul_cancel_left Matrix.nonsing_inv_mul_cancel_leftₓ'. -/
 @[simp]
 theorem nonsing_inv_mul_cancel_left (B : Matrix n m α) (h : IsUnit A.det) : A⁻¹ ⬝ (A ⬝ B) = B := by
   simp [← Matrix.mul_assoc, nonsing_inv_mul A h]
 #align matrix.nonsing_inv_mul_cancel_left Matrix.nonsing_inv_mul_cancel_left
 
+/- warning: matrix.mul_inv_of_invertible -> Matrix.mul_inv_of_invertible is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.mul_inv_of_invertible Matrix.mul_inv_of_invertibleₓ'. -/
 @[simp]
 theorem mul_inv_of_invertible [Invertible A] : A ⬝ A⁻¹ = 1 :=
   mul_nonsing_inv A (isUnit_det_of_invertible A)
 #align matrix.mul_inv_of_invertible Matrix.mul_inv_of_invertible
 
+/- warning: matrix.inv_mul_of_invertible -> Matrix.inv_mul_of_invertible is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.inv_mul_of_invertible Matrix.inv_mul_of_invertibleₓ'. -/
 @[simp]
 theorem inv_mul_of_invertible [Invertible A] : A⁻¹ ⬝ A = 1 :=
   nonsing_inv_mul A (isUnit_det_of_invertible A)
 #align matrix.inv_mul_of_invertible Matrix.inv_mul_of_invertible
 
+/- warning: matrix.mul_inv_cancel_right_of_invertible -> Matrix.mul_inv_cancel_right_of_invertible is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.mul_inv_cancel_right_of_invertible Matrix.mul_inv_cancel_right_of_invertibleₓ'. -/
 @[simp]
 theorem mul_inv_cancel_right_of_invertible (B : Matrix m n α) [Invertible A] : B ⬝ A ⬝ A⁻¹ = B :=
   mul_nonsing_inv_cancel_right A B (isUnit_det_of_invertible A)
 #align matrix.mul_inv_cancel_right_of_invertible Matrix.mul_inv_cancel_right_of_invertible
 
+/- warning: matrix.mul_inv_cancel_left_of_invertible -> Matrix.mul_inv_cancel_left_of_invertible is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.mul_inv_cancel_left_of_invertible Matrix.mul_inv_cancel_left_of_invertibleₓ'. -/
 @[simp]
 theorem mul_inv_cancel_left_of_invertible (B : Matrix n m α) [Invertible A] : A ⬝ (A⁻¹ ⬝ B) = B :=
   mul_nonsing_inv_cancel_left A B (isUnit_det_of_invertible A)
 #align matrix.mul_inv_cancel_left_of_invertible Matrix.mul_inv_cancel_left_of_invertible
 
+/- warning: matrix.inv_mul_cancel_right_of_invertible -> Matrix.inv_mul_cancel_right_of_invertible is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align matrix.inv_mul_cancel_right_of_invertible Matrix.inv_mul_cancel_right_of_invertibleₓ'. -/
 @[simp]
 theorem inv_mul_cancel_right_of_invertible (B : Matrix m n α) [Invertible A] : B ⬝ A⁻¹ ⬝ A = B :=
   nonsing_inv_mul_cancel_right A B (isUnit_det_of_invertible A)
 #align matrix.inv_mul_cancel_right_of_invertible Matrix.inv_mul_cancel_right_of_invertible
 
+/- warning: matrix.inv_mul_cancel_left_of_invertible -> Matrix.inv_mul_cancel_left_of_invertible is a dubious translation:
+lean 3 declaration is
+  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] (A : Matrix.{u2, u2, u3} n n α) (B : Matrix.{u2, u1, u3} n m α) [_inst_4 : Invertible.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.hasMul.{u3, u2} n α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.hasOne.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u3} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (AddMonoidWithOne.toOne.{u3} α (AddGroupWithOne.toAddMonoidWithOne.{u3} α (AddCommGroupWithOne.toAddGroupWithOne.{u3} α (Ring.toAddCommGroupWithOne.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) A], Eq.{succ (max u2 u1 u3)} (Matrix.{u2, u1, u3} n m α) (Matrix.mul.{u3, u2, u2, u1} n n m α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) (Inv.inv.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.hasInv.{u2, u3} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) (Matrix.mul.{u3, u2, u2, u1} n n m α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3))))) A B)) B
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align matrix.inv_mul_cancel_left_of_invertible Matrix.inv_mul_cancel_left_of_invertibleₓ'. -/
 @[simp]
 theorem inv_mul_cancel_left_of_invertible (B : Matrix n m α) [Invertible A] : A⁻¹ ⬝ (A ⬝ B) = B :=
   nonsing_inv_mul_cancel_left A B (isUnit_det_of_invertible A)
 #align matrix.inv_mul_cancel_left_of_invertible Matrix.inv_mul_cancel_left_of_invertible
 
+/- warning: matrix.inv_mul_eq_iff_eq_mul_of_invertible -> Matrix.inv_mul_eq_iff_eq_mul_of_invertible is a dubious translation:
+lean 3 declaration is
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (B : Matrix.{u1, u1, u2} n n α) (C : Matrix.{u1, u1, u2} n n α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) A], Iff (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A) B) C) (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) B (Matrix.mul.{u2, u1, u1, u1} n n n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) A C))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align matrix.inv_mul_eq_iff_eq_mul_of_invertible Matrix.inv_mul_eq_iff_eq_mul_of_invertibleₓ'. -/
 theorem inv_mul_eq_iff_eq_mul_of_invertible (A B C : Matrix n n α) [Invertible A] :
     A⁻¹ ⬝ B = C ↔ B = A ⬝ C :=
   ⟨fun h => by rw [← h, mul_inv_cancel_left_of_invertible], fun h => by
     rw [h, inv_mul_cancel_left_of_invertible]⟩
 #align matrix.inv_mul_eq_iff_eq_mul_of_invertible Matrix.inv_mul_eq_iff_eq_mul_of_invertible
 
+/- warning: matrix.mul_inv_eq_iff_eq_mul_of_invertible -> Matrix.mul_inv_eq_iff_eq_mul_of_invertible is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.mul_inv_eq_iff_eq_mul_of_invertible Matrix.mul_inv_eq_iff_eq_mul_of_invertibleₓ'. -/
 theorem mul_inv_eq_iff_eq_mul_of_invertible (A B C : Matrix n n α) [Invertible A] :
     B ⬝ A⁻¹ = C ↔ B = C ⬝ A :=
   ⟨fun h => by rw [← h, inv_mul_cancel_right_of_invertible], fun h => by
     rw [h, mul_inv_cancel_right_of_invertible]⟩
 #align matrix.mul_inv_eq_iff_eq_mul_of_invertible Matrix.mul_inv_eq_iff_eq_mul_of_invertible
 
+/- warning: matrix.nonsing_inv_cancel_or_zero -> Matrix.nonsing_inv_cancel_or_zero is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.nonsing_inv_cancel_or_zero Matrix.nonsing_inv_cancel_or_zeroₓ'. -/
 theorem nonsing_inv_cancel_or_zero : A⁻¹ ⬝ A = 1 ∧ A ⬝ A⁻¹ = 1 ∨ A⁻¹ = 0 :=
   by
   by_cases h : IsUnit A.det
@@ -407,10 +725,22 @@ theorem nonsing_inv_cancel_or_zero : A⁻¹ ⬝ A = 1 ∧ A ⬝ A⁻¹ = 1 ∨ A
   · exact Or.inr (nonsing_inv_apply_not_is_unit _ h)
 #align matrix.nonsing_inv_cancel_or_zero Matrix.nonsing_inv_cancel_or_zero
 
+/- warning: matrix.det_nonsing_inv_mul_det -> Matrix.det_nonsing_inv_mul_det is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.det_nonsing_inv_mul_det Matrix.det_nonsing_inv_mul_detₓ'. -/
 theorem det_nonsing_inv_mul_det (h : IsUnit A.det) : A⁻¹.det * A.det = 1 := by
   rw [← det_mul, A.nonsing_inv_mul h, det_one]
 #align matrix.det_nonsing_inv_mul_det Matrix.det_nonsing_inv_mul_det
 
+/- warning: matrix.det_nonsing_inv -> Matrix.det_nonsing_inv is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.det_nonsing_inv Matrix.det_nonsing_invₓ'. -/
 @[simp]
 theorem det_nonsing_inv : A⁻¹.det = Ring.inverse A.det :=
   by
@@ -423,10 +753,22 @@ theorem det_nonsing_inv : A⁻¹.det = Ring.inverse A.det :=
   · rw [Ring.inverse_non_unit _ h, nonsing_inv_apply_not_is_unit _ h, det_zero ‹_›]
 #align matrix.det_nonsing_inv Matrix.det_nonsing_inv
 
+/- warning: matrix.is_unit_nonsing_inv_det -> Matrix.isUnit_nonsing_inv_det is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.is_unit_nonsing_inv_det Matrix.isUnit_nonsing_inv_detₓ'. -/
 theorem isUnit_nonsing_inv_det (h : IsUnit A.det) : IsUnit A⁻¹.det :=
   isUnit_of_mul_eq_one _ _ (A.det_nonsing_inv_mul_det h)
 #align matrix.is_unit_nonsing_inv_det Matrix.isUnit_nonsing_inv_det
 
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+Case conversion may be inaccurate. Consider using '#align matrix.nonsing_inv_nonsing_inv Matrix.nonsing_inv_nonsing_invₓ'. -/
 @[simp]
 theorem nonsing_inv_nonsing_inv (h : IsUnit A.det) : A⁻¹⁻¹ = A :=
   calc
@@ -437,10 +779,22 @@ theorem nonsing_inv_nonsing_inv (h : IsUnit A.det) : A⁻¹⁻¹ = A :=
     
 #align matrix.nonsing_inv_nonsing_inv Matrix.nonsing_inv_nonsing_inv
 
+/- warning: matrix.is_unit_nonsing_inv_det_iff -> Matrix.isUnit_nonsing_inv_det_iff is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.is_unit_nonsing_inv_det_iff Matrix.isUnit_nonsing_inv_det_iffₓ'. -/
 theorem isUnit_nonsing_inv_det_iff {A : Matrix n n α} : IsUnit A⁻¹.det ↔ IsUnit A.det := by
   rw [Matrix.det_nonsing_inv, isUnit_ring_inverse]
 #align matrix.is_unit_nonsing_inv_det_iff Matrix.isUnit_nonsing_inv_det_iff
 
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+Case conversion may be inaccurate. Consider using '#align matrix.invertible_of_is_unit_det Matrix.invertibleOfIsUnitDetₓ'. -/
 -- `is_unit.invertible` lifts the proposition `is_unit A` to a constructive inverse of `A`.
 /-- A version of `matrix.invertible_of_det_invertible` with the inverse defeq to `A⁻¹` that is
 therefore noncomputable. -/
@@ -448,12 +802,24 @@ noncomputable def invertibleOfIsUnitDet (h : IsUnit A.det) : Invertible A :=
   ⟨A⁻¹, nonsing_inv_mul A h, mul_nonsing_inv A h⟩
 #align matrix.invertible_of_is_unit_det Matrix.invertibleOfIsUnitDet
 
+/- warning: matrix.nonsing_inv_unit -> Matrix.nonsingInvUnit is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.nonsing_inv_unit Matrix.nonsingInvUnitₓ'. -/
 /-- A version of `matrix.units_of_det_invertible` with the inverse defeq to `A⁻¹` that is therefore
 noncomputable. -/
 noncomputable def nonsingInvUnit (h : IsUnit A.det) : (Matrix n n α)ˣ :=
   @unitOfInvertible _ _ _ (invertibleOfIsUnitDet A h)
 #align matrix.nonsing_inv_unit Matrix.nonsingInvUnit
 
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+Case conversion may be inaccurate. Consider using '#align matrix.unit_of_det_invertible_eq_nonsing_inv_unit Matrix.unitOfDetInvertible_eq_nonsingInvUnitₓ'. -/
 theorem unitOfDetInvertible_eq_nonsingInvUnit [Invertible A.det] :
     unitOfDetInvertible A = nonsingInvUnit A (isUnit_of_invertible _) :=
   by
@@ -463,12 +829,24 @@ theorem unitOfDetInvertible_eq_nonsingInvUnit [Invertible A.det] :
 
 variable {A} {B}
 
+/- warning: matrix.inv_eq_left_inv -> Matrix.inv_eq_left_inv is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.inv_eq_left_inv Matrix.inv_eq_left_invₓ'. -/
 /-- If matrix A is left invertible, then its inverse equals its left inverse. -/
 theorem inv_eq_left_inv (h : B ⬝ A = 1) : A⁻¹ = B :=
   letI := invertible_of_left_inverse _ _ h
   inv_of_eq_nonsing_inv A ▸ invOf_eq_left_inv h
 #align matrix.inv_eq_left_inv Matrix.inv_eq_left_inv
 
+/- warning: matrix.inv_eq_right_inv -> Matrix.inv_eq_right_inv is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.inv_eq_right_inv Matrix.inv_eq_right_invₓ'. -/
 /-- If matrix A is right invertible, then its inverse equals its right inverse. -/
 theorem inv_eq_right_inv (h : A ⬝ B = 1) : A⁻¹ = B :=
   inv_eq_left_inv (mul_eq_one_comm.2 h)
@@ -478,21 +856,45 @@ section InvEqInv
 
 variable {C : Matrix n n α}
 
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 /-- The left inverse of matrix A is unique when existing. -/
 theorem left_inv_eq_left_inv (h : B ⬝ A = 1) (g : C ⬝ A = 1) : B = C := by
   rw [← inv_eq_left_inv h, ← inv_eq_left_inv g]
 #align matrix.left_inv_eq_left_inv Matrix.left_inv_eq_left_inv
 
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 /-- The right inverse of matrix A is unique when existing. -/
 theorem right_inv_eq_right_inv (h : A ⬝ B = 1) (g : A ⬝ C = 1) : B = C := by
   rw [← inv_eq_right_inv h, ← inv_eq_right_inv g]
 #align matrix.right_inv_eq_right_inv Matrix.right_inv_eq_right_inv
 
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 /-- The right inverse of matrix A equals the left inverse of A when they exist. -/
 theorem right_inv_eq_left_inv (h : A ⬝ B = 1) (g : C ⬝ A = 1) : B = C := by
   rw [← inv_eq_right_inv h, ← inv_eq_left_inv g]
 #align matrix.right_inv_eq_left_inv Matrix.right_inv_eq_left_inv
 
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+Case conversion may be inaccurate. Consider using '#align matrix.inv_inj Matrix.inv_injₓ'. -/
 theorem inv_inj (h : A⁻¹ = B⁻¹) (h' : IsUnit A.det) : A = B :=
   by
   refine' left_inv_eq_left_inv (mul_nonsing_inv _ h') _
@@ -505,6 +907,12 @@ end InvEqInv
 
 variable (A)
 
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+Case conversion may be inaccurate. Consider using '#align matrix.inv_zero Matrix.inv_zeroₓ'. -/
 @[simp]
 theorem inv_zero : (0 : Matrix n n α)⁻¹ = 0 :=
   by
@@ -523,14 +931,32 @@ theorem inv_zero : (0 : Matrix n n α)⁻¹ = 0 :=
 noncomputable instance : InvOneClass (Matrix n n α) :=
   { Matrix.hasOne, Matrix.hasInv with inv_one := inv_eq_left_inv (by simp) }
 
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+Case conversion may be inaccurate. Consider using '#align matrix.inv_smul Matrix.inv_smulₓ'. -/
 theorem inv_smul (k : α) [Invertible k] (h : IsUnit A.det) : (k • A)⁻¹ = ⅟ k • A⁻¹ :=
   inv_eq_left_inv (by simp [h, smul_smul])
 #align matrix.inv_smul Matrix.inv_smul
 
+/- warning: matrix.inv_smul' -> Matrix.inv_smul' is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (k : Units.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))), (IsUnit.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)) -> (Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) (HSMul.hSMul.{u2, max u1 u2, max u1 u2} (Units.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.{u1, u1, u2} n n α) (Matrix.{u1, u1, u2} n n α) (instHSMul.{u2, max u1 u2} (Units.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.{u1, u1, u2} n n α) (Units.instSMulUnits.{u2, max u1 u2} α (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.smul.{u2, u1, u1, u2} n n α α (Algebra.toSMul.{u2, u2} α α (CommRing.toCommSemiring.{u2} α _inst_3) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Algebra.id.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))) k A)) (HSMul.hSMul.{u2, max u1 u2, max u1 u2} (Units.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.{u1, u1, u2} n n α) (Matrix.{u1, u1, u2} n n α) (instHSMul.{u2, max u1 u2} (Units.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.{u1, u1, u2} n n α) (Units.instSMulUnits.{u2, max u1 u2} α (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.smul.{u2, u1, u1, u2} n n α α (Algebra.toSMul.{u2, u2} α α (CommRing.toCommSemiring.{u2} α _inst_3) (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Algebra.id.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))))) (Inv.inv.{u2} (Units.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Units.instInv.{u2} α (MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) k) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.inv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) A)))
+Case conversion may be inaccurate. Consider using '#align matrix.inv_smul' Matrix.inv_smul'ₓ'. -/
 theorem inv_smul' (k : αˣ) (h : IsUnit A.det) : (k • A)⁻¹ = k⁻¹ • A⁻¹ :=
   inv_eq_left_inv (by simp [h, smul_smul])
 #align matrix.inv_smul' Matrix.inv_smul'
 
+/- warning: matrix.inv_adjugate -> Matrix.inv_adjugate is a dubious translation:
+lean 3 declaration is
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (A : Matrix.{u1, u1, u2} n n α) (h : IsUnit.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A)), Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasInv.{u1, u2} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) _inst_3) (Matrix.adjugate.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 A)) (SMul.smul.{u2, max u1 u2} (Units.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3))) (Matrix.{u1, u1, u2} n n α) (Matrix.hasSmul.{u2, u1, u1, u2} n n (Units.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3))) α (Units.hasSmul.{u2, u2} α α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Mul.toSMul.{u2} α (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Inv.inv.{u2} (Units.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3))) (Units.hasInv.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3))) (IsUnit.unit.{u2} α (Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_1 α _inst_3 A) h)) A)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align matrix.inv_adjugate Matrix.inv_adjugateₓ'. -/
 theorem inv_adjugate (A : Matrix n n α) (h : IsUnit A.det) : (adjugate A)⁻¹ = h.Unit⁻¹ • A :=
   by
   refine' inv_eq_left_inv _
@@ -539,12 +965,24 @@ theorem inv_adjugate (A : Matrix n n α) (h : IsUnit A.det) : (adjugate A)⁻¹
 
 section Diagonal
 
+/- warning: matrix.diagonal_invertible -> Matrix.diagonalInvertible is a dubious translation:
+lean 3 declaration is
+  forall {n : Type.{u1}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] {α : Type.{u2}} [_inst_4 : NonAssocSemiring.{u2} α] (v : n -> α) [_inst_5 : Invertible.{max u1 u2} (n -> α) (Pi.instMul.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => Distrib.toHasMul.{u2} α (NonUnitalNonAssocSemiring.toDistrib.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α _inst_4)))) (Pi.instOne.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => AddMonoidWithOne.toOne.{u2} α (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} α (NonAssocSemiring.toAddCommMonoidWithOne.{u2} α _inst_4)))) v], Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (MulOneClass.toHasMul.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.nonAssocSemiring.{u2, u1} n α _inst_4 _inst_1 (fun (a : n) (b : n) => _inst_2 a b))))) (MulOneClass.toHasOne.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.nonAssocSemiring.{u2, u1} n α _inst_4 _inst_1 (fun (a : n) (b : n) => _inst_2 a b))))) (Matrix.diagonal.{u2, u1} n α (fun (i : n) (j : n) => (fun (a : n) (b : n) => (fun (a : n) (b : n) => _inst_2 a b) a b) i j) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α _inst_4))) v)
+but is expected to have type
+  forall {n : Type.{u1}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] {α : Type.{u2}} [_inst_4 : NonAssocSemiring.{u2} α] (v : n -> α) [_inst_5 : Invertible.{max u1 u2} (n -> α) (Pi.instMul.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toMul.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α _inst_4))) (Pi.instOne.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonAssocSemiring.toOne.{u2} α _inst_4)) v], Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocSemiring.toMul.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α _inst_4))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroOneClass.toZero.{u2} α (NonAssocSemiring.toMulZeroOneClass.{u2} α _inst_4)) (NonAssocSemiring.toOne.{u2} α _inst_4)) (Matrix.diagonal.{u2, u1} n α (fun (i : n) (j : n) => _inst_2 i j) (MulZeroOneClass.toZero.{u2} α (NonAssocSemiring.toMulZeroOneClass.{u2} α _inst_4)) v)
+Case conversion may be inaccurate. Consider using '#align matrix.diagonal_invertible Matrix.diagonalInvertibleₓ'. -/
 /-- `diagonal v` is invertible if `v` is -/
 def diagonalInvertible {α} [NonAssocSemiring α] (v : n → α) [Invertible v] :
     Invertible (diagonal v) :=
   Invertible.map (diagonalRingHom n α) v
 #align matrix.diagonal_invertible Matrix.diagonalInvertible
 
+/- warning: matrix.inv_of_diagonal_eq -> Matrix.invOf_diagonal_eq is a dubious translation:
+lean 3 declaration is
+  forall {n : Type.{u1}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] {α : Type.{u2}} [_inst_4 : Semiring.{u2} α] (v : n -> α) [_inst_5 : Invertible.{max u1 u2} (n -> α) (Pi.instMul.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => Distrib.toHasMul.{u2} α (NonUnitalNonAssocSemiring.toDistrib.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α _inst_4))))) (Pi.instOne.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => AddMonoidWithOne.toOne.{u2} α (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} α (NonAssocSemiring.toAddCommMonoidWithOne.{u2} α (Semiring.toNonAssocSemiring.{u2} α _inst_4))))) v] [_inst_6 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (NonUnitalNonAssocSemiring.toDistrib.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α _inst_4)))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α _inst_4)))) (AddMonoidWithOne.toOne.{u2} α (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} α (NonAssocSemiring.toAddCommMonoidWithOne.{u2} α (Semiring.toNonAssocSemiring.{u2} α _inst_4))))) (Matrix.diagonal.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α _inst_4)))) v)], Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n α) (Invertible.invOf.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (NonUnitalNonAssocSemiring.toDistrib.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α _inst_4)))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α _inst_4)))) (AddMonoidWithOne.toOne.{u2} α (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} α (NonAssocSemiring.toAddCommMonoidWithOne.{u2} α (Semiring.toNonAssocSemiring.{u2} α _inst_4))))) (Matrix.diagonal.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α _inst_4)))) v) _inst_6) (Matrix.diagonal.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α _inst_4)))) (Invertible.invOf.{max u1 u2} (n -> α) (Pi.instMul.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => Distrib.toHasMul.{u2} α (NonUnitalNonAssocSemiring.toDistrib.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α _inst_4))))) (Pi.instOne.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => AddMonoidWithOne.toOne.{u2} α (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} α (NonAssocSemiring.toAddCommMonoidWithOne.{u2} α (Semiring.toNonAssocSemiring.{u2} α _inst_4))))) v _inst_5))
+but is expected to have type
+  forall {n : Type.{u2}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] {α : Type.{u1}} [_inst_4 : Semiring.{u1} α] (v : n -> α) [_inst_5 : Invertible.{max u2 u1} (n -> α) (Pi.instMul.{u2, u1} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toMul.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α _inst_4)))) (Pi.instOne.{u2, u1} n (fun (ᾰ : n) => α) (fun (i : n) => Semiring.toOne.{u1} α _inst_4)) v] [_inst_6 : Invertible.{max u2 u1} (Matrix.{u2, u2, u1} n n α) (Matrix.instMulMatrix.{u1, u2} n α _inst_1 (NonUnitalNonAssocSemiring.toMul.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α _inst_4)))) (Matrix.one.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α _inst_4)) (Semiring.toOne.{u1} α _inst_4)) (Matrix.diagonal.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α _inst_4)) v)], Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n n α) (Invertible.invOf.{max u2 u1} (Matrix.{u2, u2, u1} n n α) (Matrix.instMulMatrix.{u1, u2} n α _inst_1 (NonUnitalNonAssocSemiring.toMul.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α _inst_4)))) (Matrix.one.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α _inst_4)) (Semiring.toOne.{u1} α _inst_4)) (Matrix.diagonal.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α _inst_4)) v) _inst_6) (Matrix.diagonal.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (MonoidWithZero.toZero.{u1} α (Semiring.toMonoidWithZero.{u1} α _inst_4)) (Invertible.invOf.{max u2 u1} (n -> α) (Pi.instMul.{u2, u1} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocSemiring.toMul.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α _inst_4)))) (Pi.instOne.{u2, u1} n (fun (ᾰ : n) => α) (fun (i : n) => Semiring.toOne.{u1} α _inst_4)) v _inst_5))
+Case conversion may be inaccurate. Consider using '#align matrix.inv_of_diagonal_eq Matrix.invOf_diagonal_eqₓ'. -/
 theorem invOf_diagonal_eq {α} [Semiring α] (v : n → α) [Invertible v] [Invertible (diagonal v)] :
     ⅟ (diagonal v) = diagonal (⅟ v) :=
   by
@@ -553,6 +991,12 @@ theorem invOf_diagonal_eq {α} [Semiring α] (v : n → α) [Invertible v] [Inve
   convert(rfl : ⅟ (diagonal v) = _)
 #align matrix.inv_of_diagonal_eq Matrix.invOf_diagonal_eq
 
+/- warning: matrix.invertible_of_diagonal_invertible -> Matrix.invertibleOfDiagonalInvertible is a dubious translation:
+lean 3 declaration is
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (v : n -> α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.diagonal.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) v)], Invertible.{max u1 u2} (n -> α) (Pi.instMul.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Pi.instOne.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) v
+but is expected to have type
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (v : n -> α) [_inst_4 : Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.diagonal.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) v)], Invertible.{max u1 u2} (n -> α) (Pi.instMul.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Pi.instOne.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) v
+Case conversion may be inaccurate. Consider using '#align matrix.invertible_of_diagonal_invertible Matrix.invertibleOfDiagonalInvertibleₓ'. -/
 /-- `v` is invertible if `diagonal v` is -/
 def invertibleOfDiagonalInvertible (v : n → α) [Invertible (diagonal v)] : Invertible v
     where
@@ -575,6 +1019,12 @@ def invertibleOfDiagonalInvertible (v : n → α) [Invertible (diagonal v)] : In
       exact mul_invOf_self _
 #align matrix.invertible_of_diagonal_invertible Matrix.invertibleOfDiagonalInvertible
 
+/- warning: matrix.diagonal_invertible_equiv_invertible -> Matrix.diagonalInvertibleEquivInvertible is a dubious translation:
+lean 3 declaration is
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (v : n -> α), Equiv.{succ (max u1 u2), succ (max u1 u2)} (Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.hasMul.{u2, u1} n α _inst_1 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.hasOne.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.diagonal.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) v)) (Invertible.{max u1 u2} (n -> α) (Pi.instMul.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Pi.instOne.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => AddMonoidWithOne.toOne.{u2} α (AddGroupWithOne.toAddMonoidWithOne.{u2} α (AddCommGroupWithOne.toAddGroupWithOne.{u2} α (Ring.toAddCommGroupWithOne.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) v)
+but is expected to have type
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] (v : n -> α), Equiv.{succ (max u1 u2), succ (max u1 u2)} (Invertible.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.instMulMatrix.{u2, u1} n α _inst_1 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) (Matrix.one.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) (NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (Matrix.diagonal.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) v)) (Invertible.{max u1 u2} (n -> α) (Pi.instMul.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Pi.instOne.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => NonAssocRing.toOne.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) v)
+Case conversion may be inaccurate. Consider using '#align matrix.diagonal_invertible_equiv_invertible Matrix.diagonalInvertibleEquivInvertibleₓ'. -/
 /-- Together `matrix.diagonal_invertible` and `matrix.invertible_of_diagonal_invertible` form an
 equivalence, although both sides of the equiv are subsingleton anyway. -/
 @[simps]
@@ -586,6 +1036,12 @@ def diagonalInvertibleEquivInvertible (v : n → α) : Invertible (diagonal v) 
   right_inv _ := Subsingleton.elim _ _
 #align matrix.diagonal_invertible_equiv_invertible Matrix.diagonalInvertibleEquivInvertible
 
+/- warning: matrix.is_unit_diagonal -> Matrix.isUnit_diagonal is a dubious translation:
+lean 3 declaration is
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {v : n -> α}, Iff (IsUnit.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.ring.{u2, u1} n α _inst_1 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toRing.{u2} α _inst_3))) (Matrix.diagonal.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u2} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))))) v)) (IsUnit.{max u1 u2} (n -> α) (Pi.monoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => Ring.toMonoid.{u2} α (CommRing.toRing.{u2} α _inst_3))) v)
+but is expected to have type
+  forall {n : Type.{u1}} {α : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : CommRing.{u2} α] {v : n -> α}, Iff (IsUnit.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n n α) (Matrix.semiring.{u2, u1} n α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) _inst_1 (fun (a : n) (b : n) => _inst_2 a b)))) (Matrix.diagonal.{u2, u1} n α (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} α (CommSemiring.toCommMonoidWithZero.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3))) v)) (IsUnit.{max u1 u2} (n -> α) (Pi.monoid.{u1, u2} n (fun (ᾰ : n) => α) (fun (i : n) => MonoidWithZero.toMonoid.{u2} α (Semiring.toMonoidWithZero.{u2} α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3))))) v)
+Case conversion may be inaccurate. Consider using '#align matrix.is_unit_diagonal Matrix.isUnit_diagonalₓ'. -/
 /-- When lowered to a prop, `matrix.diagonal_invertible_equiv_invertible` forms an `iff`. -/
 @[simp]
 theorem isUnit_diagonal {v : n → α} : IsUnit (diagonal v) ↔ IsUnit v := by
@@ -593,6 +1049,12 @@ theorem isUnit_diagonal {v : n → α} : IsUnit (diagonal v) ↔ IsUnit v := by
     (diagonal_invertible_equiv_invertible v).nonempty_congr]
 #align matrix.is_unit_diagonal Matrix.isUnit_diagonal
 
+/- warning: matrix.inv_diagonal -> Matrix.inv_diagonal is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align matrix.inv_diagonal Matrix.inv_diagonalₓ'. -/
 theorem inv_diagonal (v : n → α) : (diagonal v)⁻¹ = diagonal (Ring.inverse v) :=
   by
   rw [nonsing_inv_eq_ring_inverse]
@@ -607,6 +1069,12 @@ theorem inv_diagonal (v : n → α) : (diagonal v)⁻¹ = diagonal (Ring.inverse
 
 end Diagonal
 
+/- warning: matrix.inv_inv_inv -> Matrix.inv_inv_inv is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.inv_inv_inv Matrix.inv_inv_invₓ'. -/
 @[simp]
 theorem inv_inv_inv (A : Matrix n n α) : A⁻¹⁻¹⁻¹ = A⁻¹ :=
   by
@@ -615,6 +1083,12 @@ theorem inv_inv_inv (A : Matrix n n α) : A⁻¹⁻¹⁻¹ = A⁻¹ :=
   · simp [nonsing_inv_apply_not_is_unit _ h]
 #align matrix.inv_inv_inv Matrix.inv_inv_inv
 
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+Case conversion may be inaccurate. Consider using '#align matrix.mul_inv_rev Matrix.mul_inv_revₓ'. -/
 theorem mul_inv_rev (A B : Matrix n n α) : (A ⬝ B)⁻¹ = B⁻¹ ⬝ A⁻¹ :=
   by
   simp only [inv_def]
@@ -622,6 +1096,12 @@ theorem mul_inv_rev (A B : Matrix n n α) : (A ⬝ B)⁻¹ = B⁻¹ ⬝ A⁻¹ :
     Ring.mul_inverse_rev]
 #align matrix.mul_inv_rev Matrix.mul_inv_rev
 
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+Case conversion may be inaccurate. Consider using '#align matrix.list_prod_inv_reverse Matrix.list_prod_inv_reverseₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- A version of `list.prod_inv_reverse` for `matrix.has_inv`. -/
 theorem list_prod_inv_reverse : ∀ l : List (Matrix n n α), l.Prod⁻¹ = (l.reverse.map Inv.inv).Prod
@@ -631,6 +1111,12 @@ theorem list_prod_inv_reverse : ∀ l : List (Matrix n n α), l.Prod⁻¹ = (l.r
       Matrix.mul_eq_mul, mul_inv_rev, list_prod_inv_reverse]
 #align matrix.list_prod_inv_reverse Matrix.list_prod_inv_reverse
 
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+Case conversion may be inaccurate. Consider using '#align matrix.det_smul_inv_mul_vec_eq_cramer Matrix.det_smul_inv_mulVec_eq_cramerₓ'. -/
 /-- One form of **Cramer's rule**. See `matrix.mul_vec_cramer` for a stronger form. -/
 @[simp]
 theorem det_smul_inv_mulVec_eq_cramer (A : Matrix n n α) (b : n → α) (h : IsUnit A.det) :
@@ -639,6 +1125,12 @@ theorem det_smul_inv_mulVec_eq_cramer (A : Matrix n n α) (b : n → α) (h : Is
     h.mul_coe_inv, one_smul]
 #align matrix.det_smul_inv_mul_vec_eq_cramer Matrix.det_smul_inv_mulVec_eq_cramer
 
+/- warning: matrix.det_smul_inv_vec_mul_eq_cramer_transpose -> Matrix.det_smul_inv_vecMul_eq_cramer_transpose is a dubious translation:
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_inst_3) _inst_3 (Algebra.id.{u2} α (CommRing.toCommSemiring.{u2} α _inst_3)))) (RingHom.id.{u2} α (NonAssocRing.toNonAssocSemiring.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.cramer.{u1, u2} n α (fun (a : n) (b : n) => _inst_2 a b) _inst_1 _inst_3 (Matrix.transpose.{u2, u1, u1} n n α A)) b))
+Case conversion may be inaccurate. Consider using '#align matrix.det_smul_inv_vec_mul_eq_cramer_transpose Matrix.det_smul_inv_vecMul_eq_cramer_transposeₓ'. -/
 /-- One form of **Cramer's rule**. See `matrix.mul_vec_cramer` for a stronger form. -/
 @[simp]
 theorem det_smul_inv_vecMul_eq_cramer_transpose (A : Matrix n n α) (b : n → α) (h : IsUnit A.det) :
@@ -660,6 +1152,12 @@ variable [Fintype m]
 
 variable [DecidableEq m]
 
+/- warning: matrix.submatrix_equiv_invertible -> Matrix.submatrixEquivInvertible is a dubious translation:
+lean 3 declaration is
+  forall {m : Type.{u1}} {n : Type.{u2}} {α : Type.{u3}} [_inst_1 : Fintype.{u2} n] [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : CommRing.{u3} α] [_inst_4 : Fintype.{u1} m] [_inst_5 : DecidableEq.{succ u1} m] (A : Matrix.{u1, u1, u3} m m α) (e₁ : Equiv.{succ u2, succ u1} n m) (e₂ : Equiv.{succ u2, succ u1} n m) [_inst_6 : Invertible.{max u1 u3} (Matrix.{u1, u1, u3} m m α) (Matrix.hasMul.{u3, u1} m α _inst_4 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.hasOne.{u3, u1} m α (fun (a : m) (b : m) => _inst_5 a b) (MulZeroClass.toHasZero.{u3} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (AddMonoidWithOne.toOne.{u3} α (AddGroupWithOne.toAddMonoidWithOne.{u3} α (AddCommGroupWithOne.toAddGroupWithOne.{u3} α (Ring.toAddCommGroupWithOne.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) A], Invertible.{max u2 u3} (Matrix.{u2, u2, u3} n n α) (Matrix.hasMul.{u3, u2} n α _inst_1 (Distrib.toHasMul.{u3} α (Ring.toDistrib.{u3} α (CommRing.toRing.{u3} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} α (NonUnitalNonAssocRing.toAddCommGroup.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.hasOne.{u3, u2} n α (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u3} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} α (NonAssocRing.toNonUnitalNonAssocRing.{u3} α (Ring.toNonAssocRing.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (AddMonoidWithOne.toOne.{u3} α (AddGroupWithOne.toAddMonoidWithOne.{u3} α (AddCommGroupWithOne.toAddGroupWithOne.{u3} α (Ring.toAddCommGroupWithOne.{u3} α (CommRing.toRing.{u3} α _inst_3)))))) (Matrix.submatrix.{u3, u2, u1, u1, u2} n m m n α A (coeFn.{max 1 (max (succ u2) (succ u1)) (succ u1) (succ u2), max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} n m) (fun (_x : Equiv.{succ u2, succ u1} n m) => n -> m) (Equiv.hasCoeToFun.{succ u2, succ u1} n m) e₁) (coeFn.{max 1 (max (succ u2) (succ u1)) (succ u1) (succ u2), max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} n m) (fun (_x : Equiv.{succ u2, succ u1} n m) => n -> m) (Equiv.hasCoeToFun.{succ u2, succ u1} n m) e₂))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align matrix.submatrix_equiv_invertible Matrix.submatrixEquivInvertibleₓ'. -/
 /-- `A.submatrix e₁ e₂` is invertible if `A` is -/
 def submatrixEquivInvertible (A : Matrix m m α) (e₁ e₂ : n ≃ m) [Invertible A] :
     Invertible (A.submatrix e₁ e₂) :=
@@ -667,6 +1165,12 @@ def submatrixEquivInvertible (A : Matrix m m α) (e₁ e₂ : n ≃ m) [Invertib
     rw [Matrix.submatrix_mul_equiv, Matrix.mul_invOf_self, submatrix_one_equiv]
 #align matrix.submatrix_equiv_invertible Matrix.submatrixEquivInvertible
 
+/- warning: matrix.invertible_of_submatrix_equiv_invertible -> Matrix.invertibleOfSubmatrixEquivInvertible is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align matrix.invertible_of_submatrix_equiv_invertible Matrix.invertibleOfSubmatrixEquivInvertibleₓ'. -/
 /-- `A` is invertible if `A.submatrix e₁ e₂` is -/
 def invertibleOfSubmatrixEquivInvertible (A : Matrix m m α) (e₁ e₂ : n ≃ m)
     [Invertible (A.submatrix e₁ e₂)] : Invertible A :=
@@ -679,6 +1183,12 @@ def invertibleOfSubmatrixEquivInvertible (A : Matrix m m α) (e₁ e₂ : n ≃
     rw [Matrix.submatrix_mul_equiv, Matrix.mul_invOf_self, submatrix_one_equiv]
 #align matrix.invertible_of_submatrix_equiv_invertible Matrix.invertibleOfSubmatrixEquivInvertible
 
+/- warning: matrix.inv_of_submatrix_equiv_eq -> Matrix.invOf_submatrix_equiv_eq is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.inv_of_submatrix_equiv_eq Matrix.invOf_submatrix_equiv_eqₓ'. -/
 theorem invOf_submatrix_equiv_eq (A : Matrix m m α) (e₁ e₂ : n ≃ m) [Invertible A]
     [Invertible (A.submatrix e₁ e₂)] : ⅟ (A.submatrix e₁ e₂) = (⅟ A).submatrix e₂ e₁ :=
   by
@@ -687,6 +1197,12 @@ theorem invOf_submatrix_equiv_eq (A : Matrix m m α) (e₁ e₂ : n ≃ m) [Inve
   convert(rfl : ⅟ (A.submatrix e₁ e₂) = _)
 #align matrix.inv_of_submatrix_equiv_eq Matrix.invOf_submatrix_equiv_eq
 
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 /-- Together `matrix.submatrix_equiv_invertible` and
 `matrix.invertible_of_submatrix_equiv_invertible` form an equivalence, although both sides of the
 equiv are subsingleton anyway. -/
@@ -700,6 +1216,7 @@ def submatrixEquivInvertibleEquivInvertible (A : Matrix m m α) (e₁ e₂ : n 
   right_inv _ := Subsingleton.elim _ _
 #align matrix.submatrix_equiv_invertible_equiv_invertible Matrix.submatrixEquivInvertibleEquivInvertible
 
+#print Matrix.isUnit_submatrix_equiv /-
 /-- When lowered to a prop, `matrix.invertible_of_submatrix_equiv_invertible` forms an `iff`. -/
 @[simp]
 theorem isUnit_submatrix_equiv {A : Matrix m m α} (e₁ e₂ : n ≃ m) :
@@ -707,7 +1224,14 @@ theorem isUnit_submatrix_equiv {A : Matrix m m α} (e₁ e₂ : n ≃ m) :
   simp only [← nonempty_invertible_iff_isUnit,
     (submatrix_equiv_invertible_equiv_invertible A _ _).nonempty_congr]
 #align matrix.is_unit_submatrix_equiv Matrix.isUnit_submatrix_equiv
+-/
 
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 @[simp]
 theorem inv_submatrix_equiv (A : Matrix m m α) (e₁ e₂ : n ≃ m) :
     (A.submatrix e₁ e₂)⁻¹ = A⁻¹.submatrix e₂ e₁ :=
@@ -721,6 +1245,12 @@ theorem inv_submatrix_equiv (A : Matrix m m α) (e₁ e₂ : n ≃ m) :
       submatrix_zero, Pi.zero_apply]
 #align matrix.inv_submatrix_equiv Matrix.inv_submatrix_equiv
 
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 theorem inv_reindex (e₁ e₂ : n ≃ m) (A : Matrix n n α) : (reindex e₁ e₂ A)⁻¹ = reindex e₂ e₁ A⁻¹ :=
   inv_submatrix_equiv A e₁.symm e₂.symm
 #align matrix.inv_reindex Matrix.inv_reindex
@@ -734,11 +1264,23 @@ section Det
 
 variable [Fintype m] [DecidableEq m]
 
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+  forall {m : Type.{u1}} {α : Type.{u2}} [_inst_3 : CommRing.{u2} α] [_inst_4 : Fintype.{u1} m] [_inst_5 : DecidableEq.{succ u1} m] {M : Matrix.{u1, u1, u2} m m α}, (IsUnit.{max u1 u2} (Matrix.{u1, u1, u2} m m α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} m m α) (Matrix.ring.{u2, u1} m α _inst_4 (fun (a : m) (b : m) => _inst_5 a b) (CommRing.toRing.{u2} α _inst_3))) M) -> (forall (N : Matrix.{u1, u1, u2} m m α), Eq.{succ u2} α (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_5 a b) _inst_4 α _inst_3 (Matrix.mul.{u2, u1, u1, u1} m m m α _inst_4 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.mul.{u2, u1, u1, u1} m m m α _inst_4 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) M N) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} m m α) (Matrix.hasInv.{u1, u2} m α _inst_4 (fun (a : m) (b : m) => _inst_5 a b) _inst_3) M))) (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_5 a b) _inst_4 α _inst_3 N))
+but is expected to have type
+  forall {m : Type.{u1}} {α : Type.{u2}} [_inst_3 : CommRing.{u2} α] [_inst_4 : Fintype.{u1} m] [_inst_5 : DecidableEq.{succ u1} m] {M : Matrix.{u1, u1, u2} m m α}, (IsUnit.{max u1 u2} (Matrix.{u1, u1, u2} m m α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} m m α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} m m α) (Matrix.semiring.{u2, u1} m α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) _inst_4 (fun (a : m) (b : m) => _inst_5 a b)))) M) -> (forall (N : Matrix.{u1, u1, u2} m m α), Eq.{succ u2} α (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_5 a b) _inst_4 α _inst_3 (Matrix.mul.{u2, u1, u1, u1} m m m α _inst_4 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.mul.{u2, u1, u1, u1} m m m α _inst_4 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) M N) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} m m α) (Matrix.inv.{u1, u2} m α _inst_4 (fun (a : m) (b : m) => _inst_5 a b) _inst_3) M))) (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_5 a b) _inst_4 α _inst_3 N))
+Case conversion may be inaccurate. Consider using '#align matrix.det_conj Matrix.det_conjₓ'. -/
 /-- A variant of `matrix.det_units_conj`. -/
 theorem det_conj {M : Matrix m m α} (h : IsUnit M) (N : Matrix m m α) : det (M ⬝ N ⬝ M⁻¹) = det N :=
   by rw [← h.unit_spec, ← coe_units_inv, det_units_conj]
 #align matrix.det_conj Matrix.det_conj
 
+/- warning: matrix.det_conj' -> Matrix.det_conj' is a dubious translation:
+lean 3 declaration is
+  forall {m : Type.{u1}} {α : Type.{u2}} [_inst_3 : CommRing.{u2} α] [_inst_4 : Fintype.{u1} m] [_inst_5 : DecidableEq.{succ u1} m] {M : Matrix.{u1, u1, u2} m m α}, (IsUnit.{max u1 u2} (Matrix.{u1, u1, u2} m m α) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} m m α) (Matrix.ring.{u2, u1} m α _inst_4 (fun (a : m) (b : m) => _inst_5 a b) (CommRing.toRing.{u2} α _inst_3))) M) -> (forall (N : Matrix.{u1, u1, u2} m m α), Eq.{succ u2} α (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_5 a b) _inst_4 α _inst_3 (Matrix.mul.{u2, u1, u1, u1} m m m α _inst_4 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.mul.{u2, u1, u1, u1} m m m α _inst_4 (Distrib.toHasMul.{u2} α (Ring.toDistrib.{u2} α (CommRing.toRing.{u2} α _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toAddCommGroup.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} m m α) (Matrix.hasInv.{u1, u2} m α _inst_4 (fun (a : m) (b : m) => _inst_5 a b) _inst_3) M) N) M)) (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_5 a b) _inst_4 α _inst_3 N))
+but is expected to have type
+  forall {m : Type.{u1}} {α : Type.{u2}} [_inst_3 : CommRing.{u2} α] [_inst_4 : Fintype.{u1} m] [_inst_5 : DecidableEq.{succ u1} m] {M : Matrix.{u1, u1, u2} m m α}, (IsUnit.{max u1 u2} (Matrix.{u1, u1, u2} m m α) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} m m α) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} m m α) (Matrix.semiring.{u2, u1} m α (Ring.toSemiring.{u2} α (CommRing.toRing.{u2} α _inst_3)) _inst_4 (fun (a : m) (b : m) => _inst_5 a b)))) M) -> (forall (N : Matrix.{u1, u1, u2} m m α), Eq.{succ u2} α (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_5 a b) _inst_4 α _inst_3 (Matrix.mul.{u2, u1, u1, u1} m m m α _inst_4 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Matrix.mul.{u2, u1, u1, u1} m m m α _inst_4 (NonUnitalNonAssocRing.toMul.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} α (NonAssocRing.toNonUnitalNonAssocRing.{u2} α (Ring.toNonAssocRing.{u2} α (CommRing.toRing.{u2} α _inst_3))))) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} m m α) (Matrix.inv.{u1, u2} m α _inst_4 (fun (a : m) (b : m) => _inst_5 a b) _inst_3) M) N) M)) (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_5 a b) _inst_4 α _inst_3 N))
+Case conversion may be inaccurate. Consider using '#align matrix.det_conj' Matrix.det_conj'ₓ'. -/
 /-- A variant of `matrix.det_units_conj'`. -/
 theorem det_conj' {M : Matrix m m α} (h : IsUnit M) (N : Matrix m m α) :
     det (M⁻¹ ⬝ N ⬝ M) = det N := by rw [← h.unit_spec, ← coe_units_inv, det_units_conj']

mathlib commit https://github.com/leanprover-community/mathlib/commit/2651125b48fc5c170ab1111afd0817c903b1fc6c

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Tim Baanen, Lu-Ming Zhang
 
 ! This file was ported from Lean 3 source module linear_algebra.matrix.nonsingular_inverse
-! leanprover-community/mathlib commit e49764de5f8377071189dc4fa347ef5d6bb352b1
+! leanprover-community/mathlib commit a07a7ae98384cd6485d7825e161e528ba78ef3bc
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -727,47 +727,6 @@ theorem inv_reindex (e₁ e₂ : n ≃ m) (A : Matrix n n α) : (reindex e₁ e
 
 end Submatrix
 
-/-! ### Block matrices -/
-
-
-section Block
-
-variable [Fintype l]
-
-variable [DecidableEq l]
-
-variable [Fintype m]
-
-variable [DecidableEq m]
-
-/-- LDU decomposition of a block matrix with an invertible top-left corner, using the
-Schur complement. -/
-theorem fromBlocks_eq_of_invertible₁₁ (A : Matrix m m α) (B : Matrix m n α) (C : Matrix l m α)
-    (D : Matrix l n α) [Invertible A] :
-    fromBlocks A B C D =
-      fromBlocks 1 0 (C ⬝ ⅟ A) 1 ⬝ fromBlocks A 0 0 (D - C ⬝ ⅟ A ⬝ B) ⬝
-        fromBlocks 1 (⅟ A ⬝ B) 0 1 :=
-  by
-  simp only [from_blocks_multiply, Matrix.mul_zero, Matrix.zero_mul, add_zero, zero_add,
-    Matrix.one_mul, Matrix.mul_one, Matrix.invOf_mul_self, Matrix.mul_invOf_self_assoc,
-    Matrix.mul_invOf_mul_self_cancel, Matrix.mul_assoc, add_sub_cancel'_right]
-#align matrix.from_blocks_eq_of_invertible₁₁ Matrix.fromBlocks_eq_of_invertible₁₁
-
-/-- LDU decomposition of a block matrix with an invertible bottom-right corner, using the
-Schur complement. -/
-theorem fromBlocks_eq_of_invertible₂₂ (A : Matrix l m α) (B : Matrix l n α) (C : Matrix n m α)
-    (D : Matrix n n α) [Invertible D] :
-    fromBlocks A B C D =
-      fromBlocks 1 (B ⬝ ⅟ D) 0 1 ⬝ fromBlocks (A - B ⬝ ⅟ D ⬝ C) 0 0 D ⬝
-        fromBlocks 1 0 (⅟ D ⬝ C) 1 :=
-  (Matrix.reindex (Equiv.sumComm _ _) (Equiv.sumComm _ _)).Injective <| by
-    simpa [reindex_apply, sum_comm_symm, ← submatrix_mul_equiv _ _ _ (Equiv.sumComm n m), ←
-      submatrix_mul_equiv _ _ _ (Equiv.sumComm n l), sum_comm_apply,
-      from_blocks_submatrix_sum_swap_sum_swap] using from_blocks_eq_of_invertible₁₁ D C B A
-#align matrix.from_blocks_eq_of_invertible₂₂ Matrix.fromBlocks_eq_of_invertible₂₂
-
-end Block
-
 /-! ### More results about determinants -/
 
 
@@ -785,73 +744,6 @@ theorem det_conj' {M : Matrix m m α} (h : IsUnit M) (N : Matrix m m α) :
     det (M⁻¹ ⬝ N ⬝ M) = det N := by rw [← h.unit_spec, ← coe_units_inv, det_units_conj']
 #align matrix.det_conj' Matrix.det_conj'
 
-/-- Determinant of a 2×2 block matrix, expanded around an invertible top left element in terms of
-the Schur complement. -/
-theorem det_from_blocks₁₁ (A : Matrix m m α) (B : Matrix m n α) (C : Matrix n m α)
-    (D : Matrix n n α) [Invertible A] :
-    (Matrix.fromBlocks A B C D).det = det A * det (D - C ⬝ ⅟ A ⬝ B) := by
-  rw [from_blocks_eq_of_invertible₁₁, det_mul, det_mul, det_from_blocks_zero₂₁,
-    det_from_blocks_zero₂₁, det_from_blocks_zero₁₂, det_one, det_one, one_mul, one_mul, mul_one]
-#align matrix.det_from_blocks₁₁ Matrix.det_from_blocks₁₁
-
-@[simp]
-theorem det_fromBlocks_one₁₁ (B : Matrix m n α) (C : Matrix n m α) (D : Matrix n n α) :
-    (Matrix.fromBlocks 1 B C D).det = det (D - C ⬝ B) :=
-  by
-  haveI : Invertible (1 : Matrix m m α) := invertibleOne
-  rw [det_from_blocks₁₁, invOf_one, Matrix.mul_one, det_one, one_mul]
-#align matrix.det_from_blocks_one₁₁ Matrix.det_fromBlocks_one₁₁
-
-/-- Determinant of a 2×2 block matrix, expanded around an invertible bottom right element in terms
-of the Schur complement. -/
-theorem det_from_blocks₂₂ (A : Matrix m m α) (B : Matrix m n α) (C : Matrix n m α)
-    (D : Matrix n n α) [Invertible D] :
-    (Matrix.fromBlocks A B C D).det = det D * det (A - B ⬝ ⅟ D ⬝ C) :=
-  by
-  have : from_blocks A B C D = (from_blocks D C B A).submatrix (sum_comm _ _) (sum_comm _ _) :=
-    by
-    ext (i j)
-    cases i <;> cases j <;> rfl
-  rw [this, det_submatrix_equiv_self, det_from_blocks₁₁]
-#align matrix.det_from_blocks₂₂ Matrix.det_from_blocks₂₂
-
-@[simp]
-theorem det_fromBlocks_one₂₂ (A : Matrix m m α) (B : Matrix m n α) (C : Matrix n m α) :
-    (Matrix.fromBlocks A B C 1).det = det (A - B ⬝ C) :=
-  by
-  haveI : Invertible (1 : Matrix n n α) := invertibleOne
-  rw [det_from_blocks₂₂, invOf_one, Matrix.mul_one, det_one, one_mul]
-#align matrix.det_from_blocks_one₂₂ Matrix.det_fromBlocks_one₂₂
-
-/-- The **Weinstein–Aronszajn identity**. Note the `1` on the LHS is of shape m×m, while the `1` on
-the RHS is of shape n×n. -/
-theorem det_one_add_mul_comm (A : Matrix m n α) (B : Matrix n m α) :
-    det (1 + A ⬝ B) = det (1 + B ⬝ A) :=
-  calc
-    det (1 + A ⬝ B) = det (fromBlocks 1 (-A) B 1) := by
-      rw [det_from_blocks_one₂₂, Matrix.neg_mul, sub_neg_eq_add]
-    _ = det (1 + B ⬝ A) := by rw [det_from_blocks_one₁₁, Matrix.mul_neg, sub_neg_eq_add]
-    
-#align matrix.det_one_add_mul_comm Matrix.det_one_add_mul_comm
-
-/-- Alternate statement of the **Weinstein–Aronszajn identity** -/
-theorem det_mul_add_one_comm (A : Matrix m n α) (B : Matrix n m α) :
-    det (A ⬝ B + 1) = det (B ⬝ A + 1) := by rw [add_comm, det_one_add_mul_comm, add_comm]
-#align matrix.det_mul_add_one_comm Matrix.det_mul_add_one_comm
-
-theorem det_one_sub_mul_comm (A : Matrix m n α) (B : Matrix n m α) :
-    det (1 - A ⬝ B) = det (1 - B ⬝ A) := by
-  rw [sub_eq_add_neg, ← Matrix.neg_mul, det_one_add_mul_comm, Matrix.mul_neg, ← sub_eq_add_neg]
-#align matrix.det_one_sub_mul_comm Matrix.det_one_sub_mul_comm
-
-/-- A special case of the **Matrix determinant lemma** for when `A = I`.
-
-TODO: show this more generally. -/
-theorem det_one_add_col_mul_row (u v : m → α) : det (1 + col u ⬝ row v) = 1 + v ⬝ᵥ u := by
-  rw [det_one_add_mul_comm, det_unique, Pi.add_apply, Pi.add_apply, Matrix.one_apply_eq,
-    Matrix.row_mul_col_apply]
-#align matrix.det_one_add_col_mul_row Matrix.det_one_add_col_mul_row
-
 end Det
 
 end Matrix

mathlib commit https://github.com/leanprover-community/mathlib/commit/52932b3a083d4142e78a15dc928084a22fea9ba0

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Tim Baanen, Lu-Ming Zhang
 
 ! This file was ported from Lean 3 source module linear_algebra.matrix.nonsingular_inverse
-! leanprover-community/mathlib commit 996a85302b992a170cf7336beb4af2d8c3df688c
+! leanprover-community/mathlib commit e49764de5f8377071189dc4fa347ef5d6bb352b1
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -56,7 +56,7 @@ namespace Matrix
 
 universe u u' v
 
-variable {m : Type u} {n : Type u'} {α : Type v}
+variable {l : Type _} {m : Type u} {n : Type u'} {α : Type v}
 
 open Matrix BigOperators
 
@@ -727,6 +727,47 @@ theorem inv_reindex (e₁ e₂ : n ≃ m) (A : Matrix n n α) : (reindex e₁ e
 
 end Submatrix
 
+/-! ### Block matrices -/
+
+
+section Block
+
+variable [Fintype l]
+
+variable [DecidableEq l]
+
+variable [Fintype m]
+
+variable [DecidableEq m]
+
+/-- LDU decomposition of a block matrix with an invertible top-left corner, using the
+Schur complement. -/
+theorem fromBlocks_eq_of_invertible₁₁ (A : Matrix m m α) (B : Matrix m n α) (C : Matrix l m α)
+    (D : Matrix l n α) [Invertible A] :
+    fromBlocks A B C D =
+      fromBlocks 1 0 (C ⬝ ⅟ A) 1 ⬝ fromBlocks A 0 0 (D - C ⬝ ⅟ A ⬝ B) ⬝
+        fromBlocks 1 (⅟ A ⬝ B) 0 1 :=
+  by
+  simp only [from_blocks_multiply, Matrix.mul_zero, Matrix.zero_mul, add_zero, zero_add,
+    Matrix.one_mul, Matrix.mul_one, Matrix.invOf_mul_self, Matrix.mul_invOf_self_assoc,
+    Matrix.mul_invOf_mul_self_cancel, Matrix.mul_assoc, add_sub_cancel'_right]
+#align matrix.from_blocks_eq_of_invertible₁₁ Matrix.fromBlocks_eq_of_invertible₁₁
+
+/-- LDU decomposition of a block matrix with an invertible bottom-right corner, using the
+Schur complement. -/
+theorem fromBlocks_eq_of_invertible₂₂ (A : Matrix l m α) (B : Matrix l n α) (C : Matrix n m α)
+    (D : Matrix n n α) [Invertible D] :
+    fromBlocks A B C D =
+      fromBlocks 1 (B ⬝ ⅟ D) 0 1 ⬝ fromBlocks (A - B ⬝ ⅟ D ⬝ C) 0 0 D ⬝
+        fromBlocks 1 0 (⅟ D ⬝ C) 1 :=
+  (Matrix.reindex (Equiv.sumComm _ _) (Equiv.sumComm _ _)).Injective <| by
+    simpa [reindex_apply, sum_comm_symm, ← submatrix_mul_equiv _ _ _ (Equiv.sumComm n m), ←
+      submatrix_mul_equiv _ _ _ (Equiv.sumComm n l), sum_comm_apply,
+      from_blocks_submatrix_sum_swap_sum_swap] using from_blocks_eq_of_invertible₁₁ D C B A
+#align matrix.from_blocks_eq_of_invertible₂₂ Matrix.fromBlocks_eq_of_invertible₂₂
+
+end Block
+
 /-! ### More results about determinants -/
 
 
@@ -748,18 +789,9 @@ theorem det_conj' {M : Matrix m m α} (h : IsUnit M) (N : Matrix m m α) :
 the Schur complement. -/
 theorem det_from_blocks₁₁ (A : Matrix m m α) (B : Matrix m n α) (C : Matrix n m α)
     (D : Matrix n n α) [Invertible A] :
-    (Matrix.fromBlocks A B C D).det = det A * det (D - C ⬝ ⅟ A ⬝ B) :=
-  by
-  have :
-    from_blocks A B C D =
-      from_blocks 1 0 (C ⬝ ⅟ A) 1 ⬝ from_blocks A 0 0 (D - C ⬝ ⅟ A ⬝ B) ⬝
-        from_blocks 1 (⅟ A ⬝ B) 0 1 :=
-    by
-    simp only [from_blocks_multiply, Matrix.mul_zero, Matrix.zero_mul, add_zero, zero_add,
-      Matrix.one_mul, Matrix.mul_one, Matrix.invOf_mul_self, Matrix.mul_invOf_self_assoc,
-      Matrix.mul_invOf_mul_self_cancel, Matrix.mul_assoc, add_sub_cancel'_right]
-  rw [this, det_mul, det_mul, det_from_blocks_zero₂₁, det_from_blocks_zero₂₁,
-    det_from_blocks_zero₁₂, det_one, det_one, one_mul, one_mul, mul_one]
+    (Matrix.fromBlocks A B C D).det = det A * det (D - C ⬝ ⅟ A ⬝ B) := by
+  rw [from_blocks_eq_of_invertible₁₁, det_mul, det_mul, det_from_blocks_zero₂₁,
+    det_from_blocks_zero₂₁, det_from_blocks_zero₁₂, det_one, det_one, one_mul, one_mul, mul_one]
 #align matrix.det_from_blocks₁₁ Matrix.det_from_blocks₁₁
 
 @[simp]

mathlib commit https://github.com/leanprover-community/mathlib/commit/246f6f7989ff86bd07e1b014846f11304f33cf9e

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Tim Baanen, Lu-Ming Zhang
 
 ! This file was ported from Lean 3 source module linear_algebra.matrix.nonsingular_inverse
-! leanprover-community/mathlib commit da420a8c6dd5bdfb85c4ced85c34388f633bc6ff
+! leanprover-community/mathlib commit 996a85302b992a170cf7336beb4af2d8c3df688c
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -537,6 +537,8 @@ theorem inv_adjugate (A : Matrix n n α) (h : IsUnit A.det) : (adjugate A)⁻¹
   rw [smul_mul, mul_adjugate, Units.smul_def, smul_smul, h.coe_inv_mul, one_smul]
 #align matrix.inv_adjugate Matrix.inv_adjugate
 
+section Diagonal
+
 /-- `diagonal v` is invertible if `v` is -/
 def diagonalInvertible {α} [NonAssocSemiring α] (v : n → α) [Invertible v] :
     Invertible (diagonal v) :=
@@ -603,6 +605,8 @@ theorem inv_diagonal (v : n → α) : (diagonal v)⁻¹ = diagonal (Ring.inverse
     rw [Ring.inverse_non_unit _ h, Pi.zero_def, diagonal_zero, Ring.inverse_non_unit _ this]
 #align matrix.inv_diagonal Matrix.inv_diagonal
 
+end Diagonal
+
 @[simp]
 theorem inv_inv_inv (A : Matrix n n α) : A⁻¹⁻¹⁻¹ = A⁻¹ :=
   by
@@ -643,6 +647,86 @@ theorem det_smul_inv_vecMul_eq_cramer_transpose (A : Matrix n n α) (b : n → 
     Aᵀ.det_smul_inv_mulVec_eq_cramer _ (is_unit_det_transpose A h)]
 #align matrix.det_smul_inv_vec_mul_eq_cramer_transpose Matrix.det_smul_inv_vecMul_eq_cramer_transpose
 
+/-! ### Inverses of permutated matrices
+
+Note that the simp-normal form of `matrix.reindex` is `matrix.submatrix`, so we prove most of these
+results about only the latter.
+-/
+
+
+section Submatrix
+
+variable [Fintype m]
+
+variable [DecidableEq m]
+
+/-- `A.submatrix e₁ e₂` is invertible if `A` is -/
+def submatrixEquivInvertible (A : Matrix m m α) (e₁ e₂ : n ≃ m) [Invertible A] :
+    Invertible (A.submatrix e₁ e₂) :=
+  invertibleOfRightInverse _ ((⅟ A).submatrix e₂ e₁) <| by
+    rw [Matrix.submatrix_mul_equiv, Matrix.mul_invOf_self, submatrix_one_equiv]
+#align matrix.submatrix_equiv_invertible Matrix.submatrixEquivInvertible
+
+/-- `A` is invertible if `A.submatrix e₁ e₂` is -/
+def invertibleOfSubmatrixEquivInvertible (A : Matrix m m α) (e₁ e₂ : n ≃ m)
+    [Invertible (A.submatrix e₁ e₂)] : Invertible A :=
+  invertibleOfRightInverse _ ((⅟ (A.submatrix e₁ e₂)).submatrix e₂.symm e₁.symm) <|
+    by
+    have : A = (A.submatrix e₁ e₂).submatrix e₁.symm e₂.symm := by simp
+    conv in _ ⬝ _ =>
+      congr
+      rw [this]
+    rw [Matrix.submatrix_mul_equiv, Matrix.mul_invOf_self, submatrix_one_equiv]
+#align matrix.invertible_of_submatrix_equiv_invertible Matrix.invertibleOfSubmatrixEquivInvertible
+
+theorem invOf_submatrix_equiv_eq (A : Matrix m m α) (e₁ e₂ : n ≃ m) [Invertible A]
+    [Invertible (A.submatrix e₁ e₂)] : ⅟ (A.submatrix e₁ e₂) = (⅟ A).submatrix e₂ e₁ :=
+  by
+  letI := submatrix_equiv_invertible A e₁ e₂
+  haveI := Invertible.subsingleton (A.submatrix e₁ e₂)
+  convert(rfl : ⅟ (A.submatrix e₁ e₂) = _)
+#align matrix.inv_of_submatrix_equiv_eq Matrix.invOf_submatrix_equiv_eq
+
+/-- Together `matrix.submatrix_equiv_invertible` and
+`matrix.invertible_of_submatrix_equiv_invertible` form an equivalence, although both sides of the
+equiv are subsingleton anyway. -/
+@[simps]
+def submatrixEquivInvertibleEquivInvertible (A : Matrix m m α) (e₁ e₂ : n ≃ m) :
+    Invertible (A.submatrix e₁ e₂) ≃ Invertible A
+    where
+  toFun _ := invertible_of_submatrix_equiv_invertible A e₁ e₂
+  invFun _ := submatrix_equiv_invertible A e₁ e₂
+  left_inv _ := Subsingleton.elim _ _
+  right_inv _ := Subsingleton.elim _ _
+#align matrix.submatrix_equiv_invertible_equiv_invertible Matrix.submatrixEquivInvertibleEquivInvertible
+
+/-- When lowered to a prop, `matrix.invertible_of_submatrix_equiv_invertible` forms an `iff`. -/
+@[simp]
+theorem isUnit_submatrix_equiv {A : Matrix m m α} (e₁ e₂ : n ≃ m) :
+    IsUnit (A.submatrix e₁ e₂) ↔ IsUnit A := by
+  simp only [← nonempty_invertible_iff_isUnit,
+    (submatrix_equiv_invertible_equiv_invertible A _ _).nonempty_congr]
+#align matrix.is_unit_submatrix_equiv Matrix.isUnit_submatrix_equiv
+
+@[simp]
+theorem inv_submatrix_equiv (A : Matrix m m α) (e₁ e₂ : n ≃ m) :
+    (A.submatrix e₁ e₂)⁻¹ = A⁻¹.submatrix e₂ e₁ :=
+  by
+  by_cases h : IsUnit A
+  · cases h.nonempty_invertible
+    letI := submatrix_equiv_invertible A e₁ e₂
+    rw [← inv_of_eq_nonsing_inv, ← inv_of_eq_nonsing_inv, inv_of_submatrix_equiv_eq]
+  · have := (is_unit_submatrix_equiv e₁ e₂).Not.mpr h
+    simp_rw [nonsing_inv_eq_ring_inverse, Ring.inverse_non_unit _ h, Ring.inverse_non_unit _ this,
+      submatrix_zero, Pi.zero_apply]
+#align matrix.inv_submatrix_equiv Matrix.inv_submatrix_equiv
+
+theorem inv_reindex (e₁ e₂ : n ≃ m) (A : Matrix n n α) : (reindex e₁ e₂ A)⁻¹ = reindex e₂ e₁ A⁻¹ :=
+  inv_submatrix_equiv A e₁.symm e₂.symm
+#align matrix.inv_reindex Matrix.inv_reindex
+
+end Submatrix
+
 /-! ### More results about determinants -/
 
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d

@@ -114,7 +114,7 @@ def invertibleOfDetInvertible [Invertible A.det] : Invertible A
 theorem invOf_eq [Invertible A.det] [Invertible A] : ⅟ A = ⅟ A.det • A.adjugate :=
   by
   letI := invertible_of_det_invertible A
-  convert (rfl : ⅟ A = _)
+  convert(rfl : ⅟ A = _)
 #align matrix.inv_of_eq Matrix.invOf_eq
 
 /-- `A.det` is invertible if `A` has a left inverse. -/
@@ -141,7 +141,7 @@ def detInvertibleOfInvertible [Invertible A] : Invertible A.det :=
 theorem det_invOf [Invertible A] [Invertible A.det] : (⅟ A).det = ⅟ A.det :=
   by
   letI := det_invertible_of_invertible A
-  convert (rfl : _ = ⅟ A.det)
+  convert(rfl : _ = ⅟ A.det)
 #align matrix.det_inv_of Matrix.det_invOf
 
 /-- Together `matrix.det_invertible_of_invertible` and `matrix.invertible_of_det_invertible` form an
@@ -548,7 +548,7 @@ theorem invOf_diagonal_eq {α} [Semiring α] (v : n → α) [Invertible v] [Inve
   by
   letI := diagonal_invertible v
   haveI := Invertible.subsingleton (diagonal v)
-  convert (rfl : ⅟ (diagonal v) = _)
+  convert(rfl : ⅟ (diagonal v) = _)
 #align matrix.inv_of_diagonal_eq Matrix.invOf_diagonal_eq
 
 /-- `v` is invertible if `diagonal v` is -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/f24cc2891c0e328f0ee8c57387103aa462c44b5e

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Tim Baanen, Lu-Ming Zhang
 
 ! This file was ported from Lean 3 source module linear_algebra.matrix.nonsingular_inverse
-! leanprover-community/mathlib commit 25cf7631da8ddc2d5f957c388bf5e4b25a77d8dc
+! leanprover-community/mathlib commit da420a8c6dd5bdfb85c4ced85c34388f633bc6ff
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -547,6 +547,7 @@ theorem invOf_diagonal_eq {α} [Semiring α] (v : n → α) [Invertible v] [Inve
     ⅟ (diagonal v) = diagonal (⅟ v) :=
   by
   letI := diagonal_invertible v
+  haveI := Invertible.subsingleton (diagonal v)
   convert (rfl : ⅟ (diagonal v) = _)
 #align matrix.inv_of_diagonal_eq Matrix.invOf_diagonal_eq
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

Purely automatic replacement. If this is in any way controversial; I'm happy to just close this PR.

@@ -206,7 +206,7 @@ theorem isUnit_det_transpose (h : IsUnit A.det) : IsUnit Aᵀ.det := by
 /-! ### A noncomputable `Inv` instance  -/
 
 
-/-- The inverse of a square matrix, when it is invertible (and zero otherwise).-/
+/-- The inverse of a square matrix, when it is invertible (and zero otherwise). -/
 noncomputable instance inv : Inv (Matrix n n α) :=
   ⟨fun A => Ring.inverse A.det • A.adjugate⟩
 

.. in equivOfPiLEquivPi, coePiBasisFun.toMatrix_eq_transpose, vecMul_surjective_iff_exists_left_inverse, and mulVec_surjective_iff_exists_right_inverse

@@ -193,6 +193,8 @@ theorem det_ne_zero_of_right_inverse [Nontrivial α] (h : A * B = 1) : A.det ≠
 
 end Invertible
 
+section Inv
+
 variable [Fintype n] [DecidableEq n] [CommRing α]
 variable (A : Matrix n n α) (B : Matrix n n α)
 
@@ -352,13 +354,15 @@ lemma mul_right_inj_of_invertible [Invertible A] {x y : Matrix n m α} : A * x =
 lemma mul_left_inj_of_invertible [Invertible A] {x y : Matrix m n α} : x * A = y * A ↔ x = y :=
   (mul_left_injective_of_invertible A).eq_iff
 
+end Inv
+
 section InjectiveMul
-variable [Fintype m] [DecidableEq m]
+variable [Fintype n] [Fintype m] [DecidableEq m] [CommRing α]
 variable [Fintype l] [DecidableEq l]
 
 lemma mul_left_injective_of_inv (A : Matrix m n α) (B : Matrix n m α) (h : A * B = 1) :
-    Function.Injective (fun x : Matrix l m α => x * A) :=
-  fun _ _ g => by simpa only [Matrix.mul_assoc, Matrix.mul_one, h] using congr_arg (· * B) g
+    Function.Injective (fun x : Matrix l m α => x * A) := fun _ _ g => by
+  simpa only [Matrix.mul_assoc, Matrix.mul_one, h] using congr_arg (· * B) g
 
 lemma mul_right_injective_of_inv (A : Matrix m n α) (B : Matrix n m α) (h : A * B = 1) :
     Function.Injective (fun x : Matrix m l α => B * x) :=
@@ -368,29 +372,39 @@ end InjectiveMul
 
 section vecMul
 
-variable [Fintype m] [DecidableEq m] {K R : Type*} [Field K]
+variable [DecidableEq m] [DecidableEq n]
+
+section Semiring
 
-theorem vecMul_surjective_iff_exists_left_inverse [Semiring R] {A : Matrix m n R} :
+variable {R : Type*} [Semiring R]
+
+theorem vecMul_surjective_iff_exists_left_inverse [Fintype m] [Finite n] {A : Matrix m n R} :
     Function.Surjective A.vecMul ↔ ∃ B : Matrix n m R, B * A = 1 := by
+  cases nonempty_fintype n
   refine ⟨fun h ↦ ?_, fun ⟨B, hBA⟩ y ↦ ⟨y ᵥ* B, by simp [hBA]⟩⟩
   choose rows hrows using (h <| Pi.single · 1)
   refine ⟨Matrix.of rows, Matrix.ext fun i j => ?_⟩
   rw [mul_apply_eq_vecMul, one_eq_pi_single, ← hrows]
   rfl
 
-theorem mulVec_surjective_iff_exists_right_inverse [Semiring R] {A : Matrix m n R} :
+theorem mulVec_surjective_iff_exists_right_inverse [Finite m] [Fintype n] {A : Matrix m n R} :
     Function.Surjective A.mulVec ↔ ∃ B : Matrix n m R, A * B = 1 := by
+  cases nonempty_fintype m
   refine ⟨fun h ↦ ?_, fun ⟨B, hBA⟩ y ↦ ⟨B *ᵥ y, by simp [hBA]⟩⟩
   choose cols hcols using (h <| Pi.single · 1)
   refine ⟨(Matrix.of cols)ᵀ, Matrix.ext fun i j ↦ ?_⟩
   rw [one_eq_pi_single, Pi.single_comm, ← hcols j]
   rfl
 
-theorem vecMul_surjective_iff_isUnit {A : Matrix m m α} :
+end Semiring
+
+variable {R K : Type*} [CommRing R] [Field K] [Fintype m]
+
+theorem vecMul_surjective_iff_isUnit {A : Matrix m m R} :
     Function.Surjective A.vecMul ↔ IsUnit A := by
   rw [vecMul_surjective_iff_exists_left_inverse, exists_left_inverse_iff_isUnit]
 
-theorem mulVec_surjective_iff_isUnit {A : Matrix m m α} :
+theorem mulVec_surjective_iff_isUnit {A : Matrix m m R} :
     Function.Surjective A.mulVec ↔ IsUnit A := by
   rw [mulVec_surjective_iff_exists_right_inverse, exists_right_inverse_iff_isUnit]
 
@@ -420,11 +434,11 @@ theorem linearIndependent_cols_iff_isUnit {A : Matrix m m K} :
   rw [← transpose_transpose A, isUnit_transpose, linearIndependent_rows_iff_isUnit,
     transpose_transpose]
 
-theorem vecMul_surjective_of_invertible (A : Matrix m m α) [Invertible A] :
+theorem vecMul_surjective_of_invertible (A : Matrix m m R) [Invertible A] :
     Function.Surjective A.vecMul :=
   vecMul_surjective_iff_isUnit.2 <| isUnit_of_invertible A
 
-theorem mulVec_surjective_of_invertible (A : Matrix m m α) [Invertible A] :
+theorem mulVec_surjective_of_invertible (A : Matrix m m R) [Invertible A] :
     Function.Surjective A.mulVec :=
   mulVec_surjective_iff_isUnit.2 <| isUnit_of_invertible A
 
@@ -446,6 +460,9 @@ theorem linearIndependent_cols_of_invertible (A : Matrix m m K) [Invertible A] :
 
 end vecMul
 
+variable [Fintype n] [DecidableEq n] [CommRing α]
+variable (A : Matrix n n α) (B : Matrix n n α)
+
 theorem nonsing_inv_cancel_or_zero : A⁻¹ * A = 1 ∧ A * A⁻¹ = 1 ∨ A⁻¹ = 0 := by
   by_cases h : IsUnit A.det
   · exact Or.inl ⟨nonsing_inv_mul _ h, mul_nonsing_inv _ h⟩
@@ -760,7 +777,7 @@ end Submatrix
 
 section Det
 
-variable [Fintype m] [DecidableEq m]
+variable [Fintype m] [DecidableEq m] [CommRing α]
 
 /-- A variant of `Matrix.det_units_conj`. -/
 theorem det_conj {M : Matrix m m α} (h : IsUnit M) (N : Matrix m m α) : det (M * N * M⁻¹) = det N :=

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

@@ -65,7 +65,6 @@ open Matrix BigOperators Equiv Equiv.Perm Finset
 section Invertible
 
 variable [Fintype n] [DecidableEq n] [CommRing α]
-
 variable (A : Matrix n n α) (B : Matrix n n α)
 
 /-- If `A.det` has a constructive inverse, produce one for `A`. -/
@@ -195,7 +194,6 @@ theorem det_ne_zero_of_right_inverse [Nontrivial α] (h : A * B = 1) : A.det ≠
 end Invertible
 
 variable [Fintype n] [DecidableEq n] [CommRing α]
-
 variable (A : Matrix n n α) (B : Matrix n n α)
 
 theorem isUnit_det_transpose (h : IsUnit A.det) : IsUnit Aᵀ.det := by
@@ -690,7 +688,6 @@ results about only the latter.
 section Submatrix
 
 variable [Fintype m]
-
 variable [DecidableEq m]
 
 /-- `A.submatrix e₁ e₂` is invertible if `A` is -/

Zulip discussion: https://leanprover.zulipchat.com/#narrow/stream/113488-general/topic/Notation.20for.20mul_vec.20and.20vec_mul

Co-authored-by: Martin Dvorak <mdvorak@ista.ac.at>

@@ -374,7 +374,7 @@ variable [Fintype m] [DecidableEq m] {K R : Type*} [Field K]
 
 theorem vecMul_surjective_iff_exists_left_inverse [Semiring R] {A : Matrix m n R} :
     Function.Surjective A.vecMul ↔ ∃ B : Matrix n m R, B * A = 1 := by
-  refine ⟨fun h ↦ ?_, fun ⟨B, hBA⟩ y ↦ ⟨B.vecMul y, by simp [hBA]⟩⟩
+  refine ⟨fun h ↦ ?_, fun ⟨B, hBA⟩ y ↦ ⟨y ᵥ* B, by simp [hBA]⟩⟩
   choose rows hrows using (h <| Pi.single · 1)
   refine ⟨Matrix.of rows, Matrix.ext fun i j => ?_⟩
   rw [mul_apply_eq_vecMul, one_eq_pi_single, ← hrows]
@@ -382,7 +382,7 @@ theorem vecMul_surjective_iff_exists_left_inverse [Semiring R] {A : Matrix m n R
 
 theorem mulVec_surjective_iff_exists_right_inverse [Semiring R] {A : Matrix m n R} :
     Function.Surjective A.mulVec ↔ ∃ B : Matrix n m R, A * B = 1 := by
-  refine ⟨fun h ↦ ?_, fun ⟨B, hBA⟩ y ↦ ⟨B.mulVec y, by simp [hBA]⟩⟩
+  refine ⟨fun h ↦ ?_, fun ⟨B, hBA⟩ y ↦ ⟨B *ᵥ y, by simp [hBA]⟩⟩
   choose cols hcols using (h <| Pi.single · 1)
   refine ⟨(Matrix.of cols)ᵀ, Matrix.ext fun i j ↦ ?_⟩
   rw [one_eq_pi_single, Pi.single_comm, ← hcols j]
@@ -667,7 +667,7 @@ theorem list_prod_inv_reverse : ∀ l : List (Matrix n n α), l.prod⁻¹ = (l.r
 /-- One form of **Cramer's rule**. See `Matrix.mulVec_cramer` for a stronger form. -/
 @[simp]
 theorem det_smul_inv_mulVec_eq_cramer (A : Matrix n n α) (b : n → α) (h : IsUnit A.det) :
-    A.det • A⁻¹.mulVec b = cramer A b := by
+    A.det • A⁻¹ *ᵥ b = cramer A b := by
   rw [cramer_eq_adjugate_mulVec, A.nonsing_inv_apply h, ← smul_mulVec_assoc, smul_smul,
     h.mul_val_inv, one_smul]
 #align matrix.det_smul_inv_mul_vec_eq_cramer Matrix.det_smul_inv_mulVec_eq_cramer
@@ -675,7 +675,7 @@ theorem det_smul_inv_mulVec_eq_cramer (A : Matrix n n α) (b : n → α) (h : Is
 /-- One form of **Cramer's rule**. See `Matrix.mulVec_cramer` for a stronger form. -/
 @[simp]
 theorem det_smul_inv_vecMul_eq_cramer_transpose (A : Matrix n n α) (b : n → α) (h : IsUnit A.det) :
-    A.det • A⁻¹.vecMul b = cramer Aᵀ b := by
+    A.det • b ᵥ* A⁻¹ = cramer Aᵀ b := by
   rw [← A⁻¹.transpose_transpose, vecMul_transpose, transpose_nonsing_inv, ← det_transpose,
     Aᵀ.det_smul_inv_mulVec_eq_cramer _ (isUnit_det_transpose A h)]
 #align matrix.det_smul_inv_vec_mul_eq_cramer_transpose Matrix.det_smul_inv_vecMul_eq_cramer_transpose

I literally went through and regex'd some uses of cases', replacing them with rcases; this is meant to be a low effort PR as I hope that tools can do this in the future.

rcases is an easier replacement than cases, though with better tools we could in future do a second pass converting simple rcases added here (and existing ones) to cases.

@@ -553,7 +553,7 @@ variable (A)
 theorem inv_zero : (0 : Matrix n n α)⁻¹ = 0 := by
   cases' subsingleton_or_nontrivial α with ht ht
   · simp [eq_iff_true_of_subsingleton]
-  cases' (Fintype.card n).zero_le.eq_or_lt with hc hc
+  rcases (Fintype.card n).zero_le.eq_or_lt with hc | hc
   · rw [eq_comm, Fintype.card_eq_zero_iff] at hc
     haveI := hc
     ext i

We add some results on invertible matrices, showing that for a finite square matrix A, IsUnit A is equivalent to the surjectivity/injectivity of left/right multiplication, and to the linear independence of the set of rows/columns.

We also add a couple of lemmas about the existence of left/right inverses for nonsquare matrices, and a bit of API for mulVecLin and vecMulLinear.

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -5,6 +5,7 @@ Authors: Anne Baanen, Lu-Ming Zhang
 -/
 import Mathlib.Data.Matrix.Invertible
 import Mathlib.LinearAlgebra.Matrix.Adjugate
+import Mathlib.LinearAlgebra.FiniteDimensional
 
 #align_import linear_algebra.matrix.nonsingular_inverse from "leanprover-community/mathlib"@"722b3b152ddd5e0cf21c0a29787c76596cb6b422"
 
@@ -165,10 +166,16 @@ theorem isUnit_of_left_inverse (h : B * A = 1) : IsUnit A :=
   ⟨⟨A, B, mul_eq_one_comm.mp h, h⟩, rfl⟩
 #align matrix.is_unit_of_left_inverse Matrix.isUnit_of_left_inverse
 
+theorem exists_left_inverse_iff_isUnit : (∃ B, B * A = 1) ↔ IsUnit A :=
+  ⟨fun ⟨_, h⟩ ↦ isUnit_of_left_inverse h, fun h ↦ have := h.invertible; ⟨⅟A, invOf_mul_self' A⟩⟩
+
 theorem isUnit_of_right_inverse (h : A * B = 1) : IsUnit A :=
   ⟨⟨A, B, h, mul_eq_one_comm.mp h⟩, rfl⟩
 #align matrix.is_unit_of_right_inverse Matrix.isUnit_of_right_inverse
 
+theorem exists_right_inverse_iff_isUnit : (∃ B, A * B = 1) ↔ IsUnit A :=
+  ⟨fun ⟨_, h⟩ ↦ isUnit_of_right_inverse h, fun h ↦ have := h.invertible; ⟨⅟A, mul_invOf_self' A⟩⟩
+
 theorem isUnit_det_of_left_inverse (h : B * A = 1) : IsUnit A.det :=
   @isUnit_of_invertible _ _ _ (detInvertibleOfLeftInverse _ _ h)
 #align matrix.is_unit_det_of_left_inverse Matrix.isUnit_det_of_left_inverse
@@ -361,6 +368,86 @@ lemma mul_right_injective_of_inv (A : Matrix m n α) (B : Matrix n m α) (h : A
 
 end InjectiveMul
 
+section vecMul
+
+variable [Fintype m] [DecidableEq m] {K R : Type*} [Field K]
+
+theorem vecMul_surjective_iff_exists_left_inverse [Semiring R] {A : Matrix m n R} :
+    Function.Surjective A.vecMul ↔ ∃ B : Matrix n m R, B * A = 1 := by
+  refine ⟨fun h ↦ ?_, fun ⟨B, hBA⟩ y ↦ ⟨B.vecMul y, by simp [hBA]⟩⟩
+  choose rows hrows using (h <| Pi.single · 1)
+  refine ⟨Matrix.of rows, Matrix.ext fun i j => ?_⟩
+  rw [mul_apply_eq_vecMul, one_eq_pi_single, ← hrows]
+  rfl
+
+theorem mulVec_surjective_iff_exists_right_inverse [Semiring R] {A : Matrix m n R} :
+    Function.Surjective A.mulVec ↔ ∃ B : Matrix n m R, A * B = 1 := by
+  refine ⟨fun h ↦ ?_, fun ⟨B, hBA⟩ y ↦ ⟨B.mulVec y, by simp [hBA]⟩⟩
+  choose cols hcols using (h <| Pi.single · 1)
+  refine ⟨(Matrix.of cols)ᵀ, Matrix.ext fun i j ↦ ?_⟩
+  rw [one_eq_pi_single, Pi.single_comm, ← hcols j]
+  rfl
+
+theorem vecMul_surjective_iff_isUnit {A : Matrix m m α} :
+    Function.Surjective A.vecMul ↔ IsUnit A := by
+  rw [vecMul_surjective_iff_exists_left_inverse, exists_left_inverse_iff_isUnit]
+
+theorem mulVec_surjective_iff_isUnit {A : Matrix m m α} :
+    Function.Surjective A.mulVec ↔ IsUnit A := by
+  rw [mulVec_surjective_iff_exists_right_inverse, exists_right_inverse_iff_isUnit]
+
+theorem vecMul_injective_iff_isUnit {A : Matrix m m K} :
+    Function.Injective A.vecMul ↔ IsUnit A := by
+  refine ⟨fun h ↦ ?_, fun h ↦ ?_⟩
+  · rw [← vecMul_surjective_iff_isUnit]
+    exact LinearMap.surjective_of_injective (f := A.vecMulLinear) h
+  change Function.Injective A.vecMulLinear
+  rw [← LinearMap.ker_eq_bot, LinearMap.ker_eq_bot']
+  intro c hc
+  replace h := h.invertible
+  simpa using congr_arg A⁻¹.vecMulLinear hc
+
+theorem mulVec_injective_iff_isUnit {A : Matrix m m K} :
+    Function.Injective A.mulVec ↔ IsUnit A := by
+  rw [← isUnit_transpose, ← vecMul_injective_iff_isUnit]
+  simp_rw [vecMul_transpose]
+
+theorem linearIndependent_rows_iff_isUnit {A : Matrix m m K} :
+    LinearIndependent K (fun i ↦ A i) ↔ IsUnit A := by
+  rw [← transpose_transpose A, ← mulVec_injective_iff, ← coe_mulVecLin, mulVecLin_transpose,
+    transpose_transpose, ← vecMul_injective_iff_isUnit, coe_vecMulLinear]
+
+theorem linearIndependent_cols_iff_isUnit {A : Matrix m m K} :
+    LinearIndependent K (fun i ↦ Aᵀ i) ↔ IsUnit A := by
+  rw [← transpose_transpose A, isUnit_transpose, linearIndependent_rows_iff_isUnit,
+    transpose_transpose]
+
+theorem vecMul_surjective_of_invertible (A : Matrix m m α) [Invertible A] :
+    Function.Surjective A.vecMul :=
+  vecMul_surjective_iff_isUnit.2 <| isUnit_of_invertible A
+
+theorem mulVec_surjective_of_invertible (A : Matrix m m α) [Invertible A] :
+    Function.Surjective A.mulVec :=
+  mulVec_surjective_iff_isUnit.2 <| isUnit_of_invertible A
+
+theorem vecMul_injective_of_invertible (A : Matrix m m K) [Invertible A] :
+    Function.Injective A.vecMul :=
+  vecMul_injective_iff_isUnit.2 <| isUnit_of_invertible A
+
+theorem mulVec_injective_of_invertible (A : Matrix m m K) [Invertible A] :
+    Function.Injective A.mulVec :=
+  mulVec_injective_iff_isUnit.2 <| isUnit_of_invertible A
+
+theorem linearIndependent_rows_of_invertible (A : Matrix m m K) [Invertible A] :
+    LinearIndependent K (fun i ↦ A i) :=
+  linearIndependent_rows_iff_isUnit.2 <| isUnit_of_invertible A
+
+theorem linearIndependent_cols_of_invertible (A : Matrix m m K) [Invertible A] :
+    LinearIndependent K (fun i ↦ Aᵀ i) :=
+  linearIndependent_cols_iff_isUnit.2 <| isUnit_of_invertible A
+
+end vecMul
+
 theorem nonsing_inv_cancel_or_zero : A⁻¹ * A = 1 ∧ A * A⁻¹ = 1 ∨ A⁻¹ = 0 := by
   by_cases h : IsUnit A.det
   · exact Or.inl ⟨nonsing_inv_mul _ h, mul_nonsing_inv _ h⟩

Mathlib.Logic.Unique contains the line attribute [simp] eq_iff_true_of_subsingleton in ...:

https://github.com/leanprover-community/mathlib4/blob/96a11c7aac574c00370c2b3dab483cb676405c5d/Mathlib/Logic/Unique.lean#L255-L256

Despite what the in part may imply, this adds the lemma to the simp set "globally", including for downstream files; it is likely that attribute [local simp] eq_iff_true_of_subsingleton in ... was meant instead (or maybe scoped simp, but I think "scoped" refers to the current namespace). Indeed, the relevant lemma is not marked with @[simp] for possible slowness: https://github.com/leanprover/std4/blob/846e9e1d6bb534774d1acd2dc430e70987da3c18/Std/Logic.lean#L749. Adding it to the simp set causes the example at https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Regression.20in.20simp to slow down.

This PR changes this and fixes the relevant downstream simps. There was also one ocurrence of attribute [simp] FullSubcategory.comp_def FullSubcategory.id_def in in Mathlib.CategoryTheory.Monoidal.Subcategory but that was much easier to fix.

https://github.com/leanprover-community/mathlib4/blob/bc49eb9ba756a233370b4b68bcdedd60402f71ed/Mathlib/CategoryTheory/Monoidal/Subcategory.lean#L118-L119

@@ -465,7 +465,7 @@ variable (A)
 @[simp]
 theorem inv_zero : (0 : Matrix n n α)⁻¹ = 0 := by
   cases' subsingleton_or_nontrivial α with ht ht
-  · simp
+  · simp [eq_iff_true_of_subsingleton]
   cases' (Fintype.card n).zero_le.eq_or_lt with hc hc
   · rw [eq_comm, Fintype.card_eq_zero_iff] at hc
     haveI := hc

Replace rcases( with rcases (. Same thing for convert( and congrm(. No other change.

@@ -78,7 +78,7 @@ def invertibleOfDetInvertible [Invertible A.det] : Invertible A where
 
 theorem invOf_eq [Invertible A.det] [Invertible A] : ⅟ A = ⅟ A.det • A.adjugate := by
   letI := invertibleOfDetInvertible A
-  convert(rfl : ⅟ A = _)
+  convert (rfl : ⅟ A = _)
 #align matrix.inv_of_eq Matrix.invOf_eq
 
 /-- `A.det` is invertible if `A` has a left inverse. -/
@@ -102,7 +102,7 @@ def detInvertibleOfInvertible [Invertible A] : Invertible A.det :=
 
 theorem det_invOf [Invertible A] [Invertible A.det] : (⅟ A).det = ⅟ A.det := by
   letI := detInvertibleOfInvertible A
-  convert(rfl : _ = ⅟ A.det)
+  convert (rfl : _ = ⅟ A.det)
 #align matrix.det_inv_of Matrix.det_invOf
 
 /-- Together `Matrix.detInvertibleOfInvertible` and `Matrix.invertibleOfDetInvertible` form an
@@ -504,7 +504,7 @@ theorem invOf_diagonal_eq {α} [Semiring α] (v : n → α) [Invertible v] [Inve
     ⅟ (diagonal v) = diagonal (⅟ v) := by
   letI := diagonalInvertible v
   -- Porting note: no longer need `haveI := Invertible.subsingleton (diagonal v)`
-  convert(rfl : ⅟ (diagonal v) = _)
+  convert (rfl : ⅟ (diagonal v) = _)
 #align matrix.inv_of_diagonal_eq Matrix.invOf_diagonal_eq
 
 /-- `v` is invertible if `diagonal v` is -/
@@ -630,7 +630,7 @@ theorem invOf_submatrix_equiv_eq (A : Matrix m m α) (e₁ e₂ : n ≃ m) [Inve
     [Invertible (A.submatrix e₁ e₂)] : ⅟ (A.submatrix e₁ e₂) = (⅟ A).submatrix e₂ e₁ := by
   letI := submatrixEquivInvertible A e₁ e₂
   -- Porting note: no longer need `haveI := Invertible.subsingleton (A.submatrix e₁ e₂)`
-  convert(rfl : ⅟ (A.submatrix e₁ e₂) = _)
+  convert (rfl : ⅟ (A.submatrix e₁ e₂) = _)
 #align matrix.inv_of_submatrix_equiv_eq Matrix.invOf_submatrix_equiv_eq
 
 /-- Together `Matrix.submatrixEquivInvertible` and

I came across a few places in Mathlib that still used this name that has been deprecated for a few years now. Now we're consistent again and I don't have to suffer when encountering the wrong version :)

@@ -1,7 +1,7 @@
 /-
-Copyright (c) 2019 Tim Baanen. All rights reserved.
+Copyright (c) 2019 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Tim Baanen, Lu-Ming Zhang
+Authors: Anne Baanen, Lu-Ming Zhang
 -/
 import Mathlib.Data.Matrix.Invertible
 import Mathlib.LinearAlgebra.Matrix.Adjugate

Given two matrices $A$ and $B$ whose product is 1 $AB = 1$, then left multiplication/right multiplication with these matrices from the appropriate side is an injection.

Suggested by @Vierkantor in PR #6042

@@ -347,6 +347,20 @@ lemma mul_right_inj_of_invertible [Invertible A] {x y : Matrix n m α} : A * x =
 lemma mul_left_inj_of_invertible [Invertible A] {x y : Matrix m n α} : x * A = y * A ↔ x = y :=
   (mul_left_injective_of_invertible A).eq_iff
 
+section InjectiveMul
+variable [Fintype m] [DecidableEq m]
+variable [Fintype l] [DecidableEq l]
+
+lemma mul_left_injective_of_inv (A : Matrix m n α) (B : Matrix n m α) (h : A * B = 1) :
+    Function.Injective (fun x : Matrix l m α => x * A) :=
+  fun _ _ g => by simpa only [Matrix.mul_assoc, Matrix.mul_one, h] using congr_arg (· * B) g
+
+lemma mul_right_injective_of_inv (A : Matrix m n α) (B : Matrix n m α) (h : A * B = 1) :
+    Function.Injective (fun x : Matrix m l α => B * x) :=
+  fun _ _ g => by simpa only [← Matrix.mul_assoc, Matrix.one_mul, h] using congr_arg (A * ·) g
+
+end InjectiveMul
+
 theorem nonsing_inv_cancel_or_zero : A⁻¹ * A = 1 ∧ A * A⁻¹ = 1 ∨ A⁻¹ = 0 := by
   by_cases h : IsUnit A.det
   · exact Or.inl ⟨nonsing_inv_mul _ h, mul_nonsing_inv _ h⟩

The conjTranspose lemmas now work for non-commutative rings.

@@ -142,29 +142,6 @@ def invertibleOfRightInverse (h : A * B = 1) : Invertible A :=
   ⟨B, mul_eq_one_comm.mp h, h⟩
 #align matrix.invertible_of_right_inverse Matrix.invertibleOfRightInverse
 
-/-- The transpose of an invertible matrix is invertible. -/
-instance invertibleTranspose [Invertible A] : Invertible Aᵀ :=
-  haveI : Invertible Aᵀ.det := by simpa using detInvertibleOfInvertible A
-  invertibleOfDetInvertible Aᵀ
-#align matrix.invertible_transpose Matrix.invertibleTranspose
-
--- porting note: added because Lean can no longer find this instance automatically
-/-- The conjugate transpose of an invertible matrix is invertible. -/
-instance invertibleConjTranspose [StarRing α] [Invertible A] : Invertible Aᴴ :=
-  Invertible.star A
-
-/-- A matrix is invertible if the transpose is invertible. -/
-def invertibleOfInvertibleTranspose [Invertible Aᵀ] : Invertible A := by
-  rw [← transpose_transpose A]
-  infer_instance
-#align matrix.invertible__of_invertible_transpose Matrix.invertibleOfInvertibleTranspose
-
-/-- A matrix is invertible if the conjugate transpose is invertible. -/
-def invertibleOfInvertibleConjTranspose [StarRing α] [Invertible Aᴴ] : Invertible A := by
-  rw [← conjTranspose_conjTranspose A, ← star_eq_conjTranspose]
-  infer_instance
-#align matrix.invertible_of_invertible_conj_transpose Matrix.invertibleOfInvertibleConjTranspose
-
 /-- Given a proof that `A.det` has a constructive inverse, lift `A` to `(Matrix n n α)ˣ`-/
 def unitOfDetInvertible [Invertible A.det] : (Matrix n n α)ˣ :=
   @unitOfInvertible _ _ A (invertibleOfDetInvertible A)

The main difficulty here is that * has a slightly difference precedence to ⬝. notably around smul and neg.

The other annoyance is that ↑U ⬝ A ⬝ ↑U⁻¹ : Matrix m m 𝔸 now has to be written U.val * A * (U⁻¹).val in order to typecheck.

A downside of this change to consider: if you have a goal of A * (B * C) = (A * B) * C, mul_assoc now gives the illusion of matching, when in fact Matrix.mul_assoc is needed. Previously the distinct symbol made it easy to avoid this mistake.

On the flipside, there is now no need to rewrite by Matrix.mul_eq_mul all the time (indeed, the lemma is now removed).

@@ -71,9 +71,9 @@ variable (A : Matrix n n α) (B : Matrix n n α)
 def invertibleOfDetInvertible [Invertible A.det] : Invertible A where
   invOf := ⅟ A.det • A.adjugate
   mul_invOf_self := by
-    rw [mul_smul_comm, Matrix.mul_eq_mul, mul_adjugate, smul_smul, invOf_mul_self, one_smul]
+    rw [mul_smul_comm, mul_adjugate, smul_smul, invOf_mul_self, one_smul]
   invOf_mul_self := by
-    rw [smul_mul_assoc, Matrix.mul_eq_mul, adjugate_mul, smul_smul, invOf_mul_self, one_smul]
+    rw [smul_mul_assoc, adjugate_mul, smul_smul, invOf_mul_self, one_smul]
 #align matrix.invertible_of_det_invertible Matrix.invertibleOfDetInvertible
 
 theorem invOf_eq [Invertible A.det] [Invertible A] : ⅟ A = ⅟ A.det • A.adjugate := by
@@ -82,14 +82,14 @@ theorem invOf_eq [Invertible A.det] [Invertible A] : ⅟ A = ⅟ A.det • A.adj
 #align matrix.inv_of_eq Matrix.invOf_eq
 
 /-- `A.det` is invertible if `A` has a left inverse. -/
-def detInvertibleOfLeftInverse (h : B ⬝ A = 1) : Invertible A.det where
+def detInvertibleOfLeftInverse (h : B * A = 1) : Invertible A.det where
   invOf := B.det
   mul_invOf_self := by rw [mul_comm, ← det_mul, h, det_one]
   invOf_mul_self := by rw [← det_mul, h, det_one]
 #align matrix.det_invertible_of_left_inverse Matrix.detInvertibleOfLeftInverse
 
 /-- `A.det` is invertible if `A` has a right inverse. -/
-def detInvertibleOfRightInverse (h : A ⬝ B = 1) : Invertible A.det where
+def detInvertibleOfRightInverse (h : A * B = 1) : Invertible A.det where
   invOf := B.det
   mul_invOf_self := by rw [← det_mul, h, det_one]
   invOf_mul_self := by rw [mul_comm, ← det_mul, h, det_one]
@@ -117,28 +117,28 @@ def invertibleEquivDetInvertible : Invertible A ≃ Invertible A.det where
 
 variable {A B}
 
-theorem mul_eq_one_comm : A ⬝ B = 1 ↔ B ⬝ A = 1 :=
-  suffices ∀ A B, A ⬝ B = 1 → B ⬝ A = 1 from ⟨this A B, this B A⟩
+theorem mul_eq_one_comm : A * B = 1 ↔ B * A = 1 :=
+  suffices ∀ A B, A * B = 1 → B * A = 1 from ⟨this A B, this B A⟩
   fun A B h => by
   letI : Invertible B.det := detInvertibleOfLeftInverse _ _ h
   letI : Invertible B := invertibleOfDetInvertible B
   calc
-    B ⬝ A = B ⬝ A ⬝ (B ⬝ ⅟ B) := by rw [Matrix.mul_invOf_self, Matrix.mul_one]
-    _ = B ⬝ (A ⬝ B ⬝ ⅟ B) := by simp only [Matrix.mul_assoc]
-    _ = B ⬝ ⅟ B := by rw [h, Matrix.one_mul]
-    _ = 1 := Matrix.mul_invOf_self B
+    B * A = B * A * (B * ⅟ B) := by rw [mul_invOf_self, Matrix.mul_one]
+    _ = B * (A * B * ⅟ B) := by simp only [Matrix.mul_assoc]
+    _ = B * ⅟ B := by rw [h, Matrix.one_mul]
+    _ = 1 := mul_invOf_self B
 
 #align matrix.mul_eq_one_comm Matrix.mul_eq_one_comm
 
 variable (A B)
 
 /-- We can construct an instance of invertible A if A has a left inverse. -/
-def invertibleOfLeftInverse (h : B ⬝ A = 1) : Invertible A :=
+def invertibleOfLeftInverse (h : B * A = 1) : Invertible A :=
   ⟨B, h, mul_eq_one_comm.mp h⟩
 #align matrix.invertible_of_left_inverse Matrix.invertibleOfLeftInverse
 
 /-- We can construct an instance of invertible A if A has a right inverse. -/
-def invertibleOfRightInverse (h : A ⬝ B = 1) : Invertible A :=
+def invertibleOfRightInverse (h : A * B = 1) : Invertible A :=
   ⟨B, mul_eq_one_comm.mp h, h⟩
 #align matrix.invertible_of_right_inverse Matrix.invertibleOfRightInverse
 
@@ -184,27 +184,27 @@ theorem isUnit_det_of_invertible [Invertible A] : IsUnit A.det :=
 
 variable {A B}
 
-theorem isUnit_of_left_inverse (h : B ⬝ A = 1) : IsUnit A :=
+theorem isUnit_of_left_inverse (h : B * A = 1) : IsUnit A :=
   ⟨⟨A, B, mul_eq_one_comm.mp h, h⟩, rfl⟩
 #align matrix.is_unit_of_left_inverse Matrix.isUnit_of_left_inverse
 
-theorem isUnit_of_right_inverse (h : A ⬝ B = 1) : IsUnit A :=
+theorem isUnit_of_right_inverse (h : A * B = 1) : IsUnit A :=
   ⟨⟨A, B, h, mul_eq_one_comm.mp h⟩, rfl⟩
 #align matrix.is_unit_of_right_inverse Matrix.isUnit_of_right_inverse
 
-theorem isUnit_det_of_left_inverse (h : B ⬝ A = 1) : IsUnit A.det :=
+theorem isUnit_det_of_left_inverse (h : B * A = 1) : IsUnit A.det :=
   @isUnit_of_invertible _ _ _ (detInvertibleOfLeftInverse _ _ h)
 #align matrix.is_unit_det_of_left_inverse Matrix.isUnit_det_of_left_inverse
 
-theorem isUnit_det_of_right_inverse (h : A ⬝ B = 1) : IsUnit A.det :=
+theorem isUnit_det_of_right_inverse (h : A * B = 1) : IsUnit A.det :=
   @isUnit_of_invertible _ _ _ (detInvertibleOfRightInverse _ _ h)
 #align matrix.is_unit_det_of_right_inverse Matrix.isUnit_det_of_right_inverse
 
-theorem det_ne_zero_of_left_inverse [Nontrivial α] (h : B ⬝ A = 1) : A.det ≠ 0 :=
+theorem det_ne_zero_of_left_inverse [Nontrivial α] (h : B * A = 1) : A.det ≠ 0 :=
   (isUnit_det_of_left_inverse h).ne_zero
 #align matrix.det_ne_zero_of_left_inverse Matrix.det_ne_zero_of_left_inverse
 
-theorem det_ne_zero_of_right_inverse [Nontrivial α] (h : A ⬝ B = 1) : A.det ≠ 0 :=
+theorem det_ne_zero_of_right_inverse [Nontrivial α] (h : A * B = 1) : A.det ≠ 0 :=
   (isUnit_det_of_right_inverse h).ne_zero
 #align matrix.det_ne_zero_of_right_inverse Matrix.det_ne_zero_of_right_inverse
 
@@ -273,16 +273,16 @@ theorem conjTranspose_nonsing_inv [StarRing α] : A⁻¹ᴴ = Aᴴ⁻¹ := by
 
 /-- The `nonsing_inv` of `A` is a right inverse. -/
 @[simp]
-theorem mul_nonsing_inv (h : IsUnit A.det) : A ⬝ A⁻¹ = 1 := by
+theorem mul_nonsing_inv (h : IsUnit A.det) : A * A⁻¹ = 1 := by
   cases (A.isUnit_iff_isUnit_det.mpr h).nonempty_invertible
-  rw [← invOf_eq_nonsing_inv, Matrix.mul_invOf_self]
+  rw [← invOf_eq_nonsing_inv, mul_invOf_self]
 #align matrix.mul_nonsing_inv Matrix.mul_nonsing_inv
 
 /-- The `nonsing_inv` of `A` is a left inverse. -/
 @[simp]
-theorem nonsing_inv_mul (h : IsUnit A.det) : A⁻¹ ⬝ A = 1 := by
+theorem nonsing_inv_mul (h : IsUnit A.det) : A⁻¹ * A = 1 := by
   cases (A.isUnit_iff_isUnit_det.mpr h).nonempty_invertible
-  rw [← invOf_eq_nonsing_inv, Matrix.invOf_mul_self]
+  rw [← invOf_eq_nonsing_inv, invOf_mul_self]
 #align matrix.nonsing_inv_mul Matrix.nonsing_inv_mul
 
 instance [Invertible A] : Invertible A⁻¹ := by
@@ -295,82 +295,82 @@ theorem inv_inv_of_invertible [Invertible A] : A⁻¹⁻¹ = A := by
 #align matrix.inv_inv_of_invertible Matrix.inv_inv_of_invertible
 
 @[simp]
-theorem mul_nonsing_inv_cancel_right (B : Matrix m n α) (h : IsUnit A.det) : B ⬝ A ⬝ A⁻¹ = B := by
+theorem mul_nonsing_inv_cancel_right (B : Matrix m n α) (h : IsUnit A.det) : B * A * A⁻¹ = B := by
   simp [Matrix.mul_assoc, mul_nonsing_inv A h]
 #align matrix.mul_nonsing_inv_cancel_right Matrix.mul_nonsing_inv_cancel_right
 
 @[simp]
-theorem mul_nonsing_inv_cancel_left (B : Matrix n m α) (h : IsUnit A.det) : A ⬝ (A⁻¹ ⬝ B) = B := by
+theorem mul_nonsing_inv_cancel_left (B : Matrix n m α) (h : IsUnit A.det) : A * (A⁻¹ * B) = B := by
   simp [← Matrix.mul_assoc, mul_nonsing_inv A h]
 #align matrix.mul_nonsing_inv_cancel_left Matrix.mul_nonsing_inv_cancel_left
 
 @[simp]
-theorem nonsing_inv_mul_cancel_right (B : Matrix m n α) (h : IsUnit A.det) : B ⬝ A⁻¹ ⬝ A = B := by
+theorem nonsing_inv_mul_cancel_right (B : Matrix m n α) (h : IsUnit A.det) : B * A⁻¹ * A = B := by
   simp [Matrix.mul_assoc, nonsing_inv_mul A h]
 #align matrix.nonsing_inv_mul_cancel_right Matrix.nonsing_inv_mul_cancel_right
 
 @[simp]
-theorem nonsing_inv_mul_cancel_left (B : Matrix n m α) (h : IsUnit A.det) : A⁻¹ ⬝ (A ⬝ B) = B := by
+theorem nonsing_inv_mul_cancel_left (B : Matrix n m α) (h : IsUnit A.det) : A⁻¹ * (A * B) = B := by
   simp [← Matrix.mul_assoc, nonsing_inv_mul A h]
 #align matrix.nonsing_inv_mul_cancel_left Matrix.nonsing_inv_mul_cancel_left
 
 @[simp]
-theorem mul_inv_of_invertible [Invertible A] : A ⬝ A⁻¹ = 1 :=
+theorem mul_inv_of_invertible [Invertible A] : A * A⁻¹ = 1 :=
   mul_nonsing_inv A (isUnit_det_of_invertible A)
 #align matrix.mul_inv_of_invertible Matrix.mul_inv_of_invertible
 
 @[simp]
-theorem inv_mul_of_invertible [Invertible A] : A⁻¹ ⬝ A = 1 :=
+theorem inv_mul_of_invertible [Invertible A] : A⁻¹ * A = 1 :=
   nonsing_inv_mul A (isUnit_det_of_invertible A)
 #align matrix.inv_mul_of_invertible Matrix.inv_mul_of_invertible
 
 @[simp]
-theorem mul_inv_cancel_right_of_invertible (B : Matrix m n α) [Invertible A] : B ⬝ A ⬝ A⁻¹ = B :=
+theorem mul_inv_cancel_right_of_invertible (B : Matrix m n α) [Invertible A] : B * A * A⁻¹ = B :=
   mul_nonsing_inv_cancel_right A B (isUnit_det_of_invertible A)
 #align matrix.mul_inv_cancel_right_of_invertible Matrix.mul_inv_cancel_right_of_invertible
 
 @[simp]
-theorem mul_inv_cancel_left_of_invertible (B : Matrix n m α) [Invertible A] : A ⬝ (A⁻¹ ⬝ B) = B :=
+theorem mul_inv_cancel_left_of_invertible (B : Matrix n m α) [Invertible A] : A * (A⁻¹ * B) = B :=
   mul_nonsing_inv_cancel_left A B (isUnit_det_of_invertible A)
 #align matrix.mul_inv_cancel_left_of_invertible Matrix.mul_inv_cancel_left_of_invertible
 
 @[simp]
-theorem inv_mul_cancel_right_of_invertible (B : Matrix m n α) [Invertible A] : B ⬝ A⁻¹ ⬝ A = B :=
+theorem inv_mul_cancel_right_of_invertible (B : Matrix m n α) [Invertible A] : B * A⁻¹ * A = B :=
   nonsing_inv_mul_cancel_right A B (isUnit_det_of_invertible A)
 #align matrix.inv_mul_cancel_right_of_invertible Matrix.inv_mul_cancel_right_of_invertible
 
 @[simp]
-theorem inv_mul_cancel_left_of_invertible (B : Matrix n m α) [Invertible A] : A⁻¹ ⬝ (A ⬝ B) = B :=
+theorem inv_mul_cancel_left_of_invertible (B : Matrix n m α) [Invertible A] : A⁻¹ * (A * B) = B :=
   nonsing_inv_mul_cancel_left A B (isUnit_det_of_invertible A)
 #align matrix.inv_mul_cancel_left_of_invertible Matrix.inv_mul_cancel_left_of_invertible
 
 theorem inv_mul_eq_iff_eq_mul_of_invertible (A B C : Matrix n n α) [Invertible A] :
-    A⁻¹ ⬝ B = C ↔ B = A ⬝ C :=
+    A⁻¹ * B = C ↔ B = A * C :=
   ⟨fun h => by rw [← h, mul_inv_cancel_left_of_invertible],
    fun h => by rw [h, inv_mul_cancel_left_of_invertible]⟩
 #align matrix.inv_mul_eq_iff_eq_mul_of_invertible Matrix.inv_mul_eq_iff_eq_mul_of_invertible
 
 theorem mul_inv_eq_iff_eq_mul_of_invertible (A B C : Matrix n n α) [Invertible A] :
-    B ⬝ A⁻¹ = C ↔ B = C ⬝ A :=
+    B * A⁻¹ = C ↔ B = C * A :=
   ⟨fun h => by rw [← h, inv_mul_cancel_right_of_invertible],
    fun h => by rw [h, mul_inv_cancel_right_of_invertible]⟩
 #align matrix.mul_inv_eq_iff_eq_mul_of_invertible Matrix.mul_inv_eq_iff_eq_mul_of_invertible
 
 lemma mul_right_injective_of_invertible [Invertible A] :
-    Function.Injective (fun (x : Matrix n m α) => A ⬝ x) :=
-  fun _ _ h => by simpa only [inv_mul_cancel_left_of_invertible] using congr_arg (A⁻¹ ⬝ ·) h
+    Function.Injective (fun (x : Matrix n m α) => A * x) :=
+  fun _ _ h => by simpa only [inv_mul_cancel_left_of_invertible] using congr_arg (A⁻¹ * ·) h
 
 lemma mul_left_injective_of_invertible [Invertible A] :
-    Function.Injective (fun (x : Matrix m n α) => x ⬝ A) :=
-  fun a x hax => by simpa only [mul_inv_cancel_right_of_invertible] using congr_arg (· ⬝ A⁻¹) hax
+    Function.Injective (fun (x : Matrix m n α) => x * A) :=
+  fun a x hax => by simpa only [mul_inv_cancel_right_of_invertible] using congr_arg (· * A⁻¹) hax
 
-lemma mul_right_inj_of_invertible [Invertible A] {x y : Matrix n m α} : A ⬝ x = A ⬝ y ↔ x = y :=
+lemma mul_right_inj_of_invertible [Invertible A] {x y : Matrix n m α} : A * x = A * y ↔ x = y :=
   (mul_right_injective_of_invertible A).eq_iff
 
-lemma mul_left_inj_of_invertible [Invertible A] {x y : Matrix m n α} : x ⬝ A = y ⬝ A ↔ x = y :=
+lemma mul_left_inj_of_invertible [Invertible A] {x y : Matrix m n α} : x * A = y * A ↔ x = y :=
   (mul_left_injective_of_invertible A).eq_iff
 
-theorem nonsing_inv_cancel_or_zero : A⁻¹ ⬝ A = 1 ∧ A ⬝ A⁻¹ = 1 ∨ A⁻¹ = 0 := by
+theorem nonsing_inv_cancel_or_zero : A⁻¹ * A = 1 ∧ A * A⁻¹ = 1 ∨ A⁻¹ = 0 := by
   by_cases h : IsUnit A.det
   · exact Or.inl ⟨nonsing_inv_mul _ h, mul_nonsing_inv _ h⟩
   · exact Or.inr (nonsing_inv_apply_not_isUnit _ h)
@@ -398,8 +398,8 @@ theorem isUnit_nonsing_inv_det (h : IsUnit A.det) : IsUnit A⁻¹.det :=
 @[simp]
 theorem nonsing_inv_nonsing_inv (h : IsUnit A.det) : A⁻¹⁻¹ = A :=
   calc
-    A⁻¹⁻¹ = 1 ⬝ A⁻¹⁻¹ := by rw [Matrix.one_mul]
-    _ = A ⬝ A⁻¹ ⬝ A⁻¹⁻¹ := by rw [A.mul_nonsing_inv h]
+    A⁻¹⁻¹ = 1 * A⁻¹⁻¹ := by rw [Matrix.one_mul]
+    _ = A * A⁻¹ * A⁻¹⁻¹ := by rw [A.mul_nonsing_inv h]
     _ = A := by
       rw [Matrix.mul_assoc, A⁻¹.mul_nonsing_inv (A.isUnit_nonsing_inv_det h), Matrix.mul_one]
 
@@ -431,13 +431,13 @@ theorem unitOfDetInvertible_eq_nonsingInvUnit [Invertible A.det] :
 variable {A} {B}
 
 /-- If matrix A is left invertible, then its inverse equals its left inverse. -/
-theorem inv_eq_left_inv (h : B ⬝ A = 1) : A⁻¹ = B :=
+theorem inv_eq_left_inv (h : B * A = 1) : A⁻¹ = B :=
   letI := invertibleOfLeftInverse _ _ h
   invOf_eq_nonsing_inv A ▸ invOf_eq_left_inv h
 #align matrix.inv_eq_left_inv Matrix.inv_eq_left_inv
 
 /-- If matrix A is right invertible, then its inverse equals its right inverse. -/
-theorem inv_eq_right_inv (h : A ⬝ B = 1) : A⁻¹ = B :=
+theorem inv_eq_right_inv (h : A * B = 1) : A⁻¹ = B :=
   inv_eq_left_inv (mul_eq_one_comm.2 h)
 #align matrix.inv_eq_right_inv Matrix.inv_eq_right_inv
 
@@ -446,17 +446,17 @@ section InvEqInv
 variable {C : Matrix n n α}
 
 /-- The left inverse of matrix A is unique when existing. -/
-theorem left_inv_eq_left_inv (h : B ⬝ A = 1) (g : C ⬝ A = 1) : B = C := by
+theorem left_inv_eq_left_inv (h : B * A = 1) (g : C * A = 1) : B = C := by
   rw [← inv_eq_left_inv h, ← inv_eq_left_inv g]
 #align matrix.left_inv_eq_left_inv Matrix.left_inv_eq_left_inv
 
 /-- The right inverse of matrix A is unique when existing. -/
-theorem right_inv_eq_right_inv (h : A ⬝ B = 1) (g : A ⬝ C = 1) : B = C := by
+theorem right_inv_eq_right_inv (h : A * B = 1) (g : A * C = 1) : B = C := by
   rw [← inv_eq_right_inv h, ← inv_eq_right_inv g]
 #align matrix.right_inv_eq_right_inv Matrix.right_inv_eq_right_inv
 
 /-- The right inverse of matrix A equals the left inverse of A when they exist. -/
-theorem right_inv_eq_left_inv (h : A ⬝ B = 1) (g : C ⬝ A = 1) : B = C := by
+theorem right_inv_eq_left_inv (h : A * B = 1) (g : C * A = 1) : B = C := by
   rw [← inv_eq_right_inv h, ← inv_eq_left_inv g]
 #align matrix.right_inv_eq_left_inv Matrix.right_inv_eq_left_inv
 
@@ -572,7 +572,7 @@ theorem inv_inv_inv (A : Matrix n n α) : A⁻¹⁻¹⁻¹ = A⁻¹ := by
   · simp [nonsing_inv_apply_not_isUnit _ h]
 #align matrix.inv_inv_inv Matrix.inv_inv_inv
 
-theorem mul_inv_rev (A B : Matrix n n α) : (A ⬝ B)⁻¹ = B⁻¹ ⬝ A⁻¹ := by
+theorem mul_inv_rev (A B : Matrix n n α) : (A * B)⁻¹ = B⁻¹ * A⁻¹ := by
   simp only [inv_def]
   rw [Matrix.smul_mul, Matrix.mul_smul, smul_smul, det_mul, adjugate_mul_distrib,
     Ring.mul_inverse_rev]
@@ -582,8 +582,8 @@ theorem mul_inv_rev (A B : Matrix n n α) : (A ⬝ B)⁻¹ = B⁻¹ ⬝ A⁻¹ :
 theorem list_prod_inv_reverse : ∀ l : List (Matrix n n α), l.prod⁻¹ = (l.reverse.map Inv.inv).prod
   | [] => by rw [List.reverse_nil, List.map_nil, List.prod_nil, inv_one]
   | A::Xs => by
-    rw [List.reverse_cons', List.map_concat, List.prod_concat, List.prod_cons, Matrix.mul_eq_mul,
-      Matrix.mul_eq_mul, mul_inv_rev, list_prod_inv_reverse Xs]
+    rw [List.reverse_cons', List.map_concat, List.prod_concat, List.prod_cons,
+      mul_inv_rev, list_prod_inv_reverse Xs]
 #align matrix.list_prod_inv_reverse Matrix.list_prod_inv_reverse
 
 /-- One form of **Cramer's rule**. See `Matrix.mulVec_cramer` for a stronger form. -/
@@ -619,7 +619,7 @@ variable [DecidableEq m]
 def submatrixEquivInvertible (A : Matrix m m α) (e₁ e₂ : n ≃ m) [Invertible A] :
     Invertible (A.submatrix e₁ e₂) :=
   invertibleOfRightInverse _ ((⅟ A).submatrix e₂ e₁) <| by
-    rw [Matrix.submatrix_mul_equiv, Matrix.mul_invOf_self, submatrix_one_equiv]
+    rw [Matrix.submatrix_mul_equiv, mul_invOf_self, submatrix_one_equiv]
 #align matrix.submatrix_equiv_invertible Matrix.submatrixEquivInvertible
 
 /-- `A` is invertible if `A.submatrix e₁ e₂` is -/
@@ -628,11 +628,11 @@ def invertibleOfSubmatrixEquivInvertible (A : Matrix m m α) (e₁ e₂ : n ≃
   invertibleOfRightInverse _ ((⅟ (A.submatrix e₁ e₂)).submatrix e₂.symm e₁.symm) <| by
     have : A = (A.submatrix e₁ e₂).submatrix e₁.symm e₂.symm := by simp
     -- Porting note: was
-    -- conv in _ ⬝ _ =>
+    -- conv in _ * _ =>
     --   congr
     --   rw [this]
-    rw [congr_arg₂ (· ⬝ ·) this rfl]
-    rw [Matrix.submatrix_mul_equiv, Matrix.mul_invOf_self, submatrix_one_equiv]
+    rw [congr_arg₂ (· * ·) this rfl]
+    rw [Matrix.submatrix_mul_equiv, mul_invOf_self, submatrix_one_equiv]
 #align matrix.invertible_of_submatrix_equiv_invertible Matrix.invertibleOfSubmatrixEquivInvertible
 
 theorem invOf_submatrix_equiv_eq (A : Matrix m m α) (e₁ e₂ : n ≃ m) [Invertible A]
@@ -688,13 +688,13 @@ section Det
 variable [Fintype m] [DecidableEq m]
 
 /-- A variant of `Matrix.det_units_conj`. -/
-theorem det_conj {M : Matrix m m α} (h : IsUnit M) (N : Matrix m m α) : det (M ⬝ N ⬝ M⁻¹) = det N :=
+theorem det_conj {M : Matrix m m α} (h : IsUnit M) (N : Matrix m m α) : det (M * N * M⁻¹) = det N :=
   by rw [← h.unit_spec, ← coe_units_inv, det_units_conj]
 #align matrix.det_conj Matrix.det_conj
 
 /-- A variant of `Matrix.det_units_conj'`. -/
 theorem det_conj' {M : Matrix m m α} (h : IsUnit M) (N : Matrix m m α) :
-    det (M⁻¹ ⬝ N ⬝ M) = det N := by rw [← h.unit_spec, ← coe_units_inv, det_units_conj']
+    det (M⁻¹ * N * M) = det N := by rw [← h.unit_spec, ← coe_units_inv, det_units_conj']
 #align matrix.det_conj' Matrix.det_conj'
 
 end Det

Multiplication by invertible matrices from the left or right is injective. Note that mul_left_injective₀ and friends don't apply because they would require similar (square) matrices.

@@ -356,6 +356,20 @@ theorem mul_inv_eq_iff_eq_mul_of_invertible (A B C : Matrix n n α) [Invertible
    fun h => by rw [h, mul_inv_cancel_right_of_invertible]⟩
 #align matrix.mul_inv_eq_iff_eq_mul_of_invertible Matrix.mul_inv_eq_iff_eq_mul_of_invertible
 
+lemma mul_right_injective_of_invertible [Invertible A] :
+    Function.Injective (fun (x : Matrix n m α) => A ⬝ x) :=
+  fun _ _ h => by simpa only [inv_mul_cancel_left_of_invertible] using congr_arg (A⁻¹ ⬝ ·) h
+
+lemma mul_left_injective_of_invertible [Invertible A] :
+    Function.Injective (fun (x : Matrix m n α) => x ⬝ A) :=
+  fun a x hax => by simpa only [mul_inv_cancel_right_of_invertible] using congr_arg (· ⬝ A⁻¹) hax
+
+lemma mul_right_inj_of_invertible [Invertible A] {x y : Matrix n m α} : A ⬝ x = A ⬝ y ↔ x = y :=
+  (mul_right_injective_of_invertible A).eq_iff
+
+lemma mul_left_inj_of_invertible [Invertible A] {x y : Matrix m n α} : x ⬝ A = y ⬝ A ↔ x = y :=
+  (mul_left_injective_of_invertible A).eq_iff
+
 theorem nonsing_inv_cancel_or_zero : A⁻¹ ⬝ A = 1 ∧ A ⬝ A⁻¹ = 1 ∨ A⁻¹ = 0 := by
   by_cases h : IsUnit A.det
   · exact Or.inl ⟨nonsing_inv_mul _ h, mul_nonsing_inv _ h⟩

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

@@ -54,7 +54,7 @@ namespace Matrix
 
 universe u u' v
 
-variable {l : Type _} {m : Type u} {n : Type u'} {α : Type v}
+variable {l : Type*} {m : Type u} {n : Type u'} {α : Type v}
 
 open Matrix BigOperators Equiv Equiv.Perm Finset
 

• depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -2,15 +2,12 @@
 Copyright (c) 2019 Tim Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Tim Baanen, Lu-Ming Zhang
-
-! This file was ported from Lean 3 source module linear_algebra.matrix.nonsingular_inverse
-! leanprover-community/mathlib commit 722b3b152ddd5e0cf21c0a29787c76596cb6b422
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Matrix.Invertible
 import Mathlib.LinearAlgebra.Matrix.Adjugate
 
+#align_import linear_algebra.matrix.nonsingular_inverse from "leanprover-community/mathlib"@"722b3b152ddd5e0cf21c0a29787c76596cb6b422"
+
 /-!
 # Nonsingular inverses
 

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

@@ -4,10 +4,11 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Tim Baanen, Lu-Ming Zhang
 
 ! This file was ported from Lean 3 source module linear_algebra.matrix.nonsingular_inverse
-! leanprover-community/mathlib commit a07a7ae98384cd6485d7825e161e528ba78ef3bc
+! leanprover-community/mathlib commit 722b3b152ddd5e0cf21c0a29787c76596cb6b422
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
+import Mathlib.Data.Matrix.Invertible
 import Mathlib.LinearAlgebra.Matrix.Adjugate
 
 /-!
@@ -67,36 +68,6 @@ section Invertible
 
 variable [Fintype n] [DecidableEq n] [CommRing α]
 
-/-- A copy of `invOf_mul_self` using `⬝` not `*`. -/
-protected theorem invOf_mul_self (A : Matrix n n α) [Invertible A] : ⅟ A ⬝ A = 1 :=
-  invOf_mul_self A
-#align matrix.inv_of_mul_self Matrix.invOf_mul_self
-
-/-- A copy of `mul_invOf_self` using `⬝` not `*`. -/
-protected theorem mul_invOf_self (A : Matrix n n α) [Invertible A] : A ⬝ ⅟ A = 1 :=
-  mul_invOf_self A
-#align matrix.mul_inv_of_self Matrix.mul_invOf_self
-
-/-- A copy of `invOf_mul_self_assoc` using `⬝` not `*`. -/
-protected theorem invOf_mul_self_assoc (A : Matrix n n α) (B : Matrix n m α) [Invertible A] :
-    ⅟ A ⬝ (A ⬝ B) = B := by rw [← Matrix.mul_assoc, Matrix.invOf_mul_self, Matrix.one_mul]
-#align matrix.inv_of_mul_self_assoc Matrix.invOf_mul_self_assoc
-
-/-- A copy of `mul_invOf_self_assoc` using `⬝` not `*`. -/
-protected theorem mul_invOf_self_assoc (A : Matrix n n α) (B : Matrix n m α) [Invertible A] :
-    A ⬝ (⅟ A ⬝ B) = B := by rw [← Matrix.mul_assoc, Matrix.mul_invOf_self, Matrix.one_mul]
-#align matrix.mul_inv_of_self_assoc Matrix.mul_invOf_self_assoc
-
-/-- A copy of `mul_invOf_mul_self_cancel` using `⬝` not `*`. -/
-protected theorem mul_invOf_mul_self_cancel (A : Matrix m n α) (B : Matrix n n α) [Invertible B] :
-    A ⬝ ⅟ B ⬝ B = A := by rw [Matrix.mul_assoc, Matrix.invOf_mul_self, Matrix.mul_one]
-#align matrix.mul_inv_of_mul_self_cancel Matrix.mul_invOf_mul_self_cancel
-
-/-- A copy of `mul_mul_invOf_self_cancel` using `⬝` not `*`. -/
-protected theorem mul_mul_invOf_self_cancel (A : Matrix m n α) (B : Matrix n n α) [Invertible B] :
-    A ⬝ B ⬝ ⅟ B = A := by rw [Matrix.mul_assoc, Matrix.mul_invOf_self, Matrix.mul_one]
-#align matrix.mul_mul_inv_of_self_cancel Matrix.mul_mul_invOf_self_cancel
-
 variable (A : Matrix n n α) (B : Matrix n n α)
 
 /-- If `A.det` has a constructive inverse, produce one for `A`. -/

• depends on: #4920
• depends on: #5058
• depends on: #5059
• depends on: #5060

@@ -180,6 +180,11 @@ instance invertibleTranspose [Invertible A] : Invertible Aᵀ :=
   invertibleOfDetInvertible Aᵀ
 #align matrix.invertible_transpose Matrix.invertibleTranspose
 
+-- porting note: added because Lean can no longer find this instance automatically
+/-- The conjugate transpose of an invertible matrix is invertible. -/
+instance invertibleConjTranspose [StarRing α] [Invertible A] : Invertible Aᴴ :=
+  Invertible.star A
+
 /-- A matrix is invertible if the transpose is invertible. -/
 def invertibleOfInvertibleTranspose [Invertible Aᵀ] : Invertible A := by
   rw [← transpose_transpose A]

Now that leanprover/lean4#2210 has been merged, this PR:

• removes all the set_option synthInstance.etaExperiment true commands (and some etaExperiment% term elaborators)
• removes many but not quite all set_option maxHeartbeats commands
• makes various other changes required to cope with leanprover/lean4#2210.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Matthew Ballard <matt@mrb.email>

@@ -293,7 +293,6 @@ theorem transpose_nonsing_inv : A⁻¹ᵀ = Aᵀ⁻¹ := by
   rw [inv_def, inv_def, transpose_smul, det_transpose, adjugate_transpose]
 #align matrix.transpose_nonsing_inv Matrix.transpose_nonsing_inv
 
-set_option synthInstance.etaExperiment true in
 theorem conjTranspose_nonsing_inv [StarRing α] : A⁻¹ᴴ = Aᴴ⁻¹ := by
   rw [inv_def, inv_def, conjTranspose_smul, det_conjTranspose, adjugate_conjTranspose,
     Ring.inverse_star]
@@ -502,17 +501,14 @@ theorem inv_zero : (0 : Matrix n n α)⁻¹ = 0 := by
 noncomputable instance : InvOneClass (Matrix n n α) :=
   { Matrix.one, Matrix.inv with inv_one := inv_eq_left_inv (by simp) }
 
-set_option synthInstance.etaExperiment true in
 theorem inv_smul (k : α) [Invertible k] (h : IsUnit A.det) : (k • A)⁻¹ = ⅟ k • A⁻¹ :=
   inv_eq_left_inv (by simp [h, smul_smul])
 #align matrix.inv_smul Matrix.inv_smul
 
-set_option synthInstance.etaExperiment true in
 theorem inv_smul' (k : αˣ) (h : IsUnit A.det) : (k • A)⁻¹ = k⁻¹ • A⁻¹ :=
   inv_eq_left_inv (by simp [h, smul_smul])
 #align matrix.inv_smul' Matrix.inv_smul'
 
-set_option synthInstance.etaExperiment true in
 theorem inv_adjugate (A : Matrix n n α) (h : IsUnit A.det) : (adjugate A)⁻¹ = h.unit⁻¹ • A := by
   refine' inv_eq_left_inv _
   rw [smul_mul, mul_adjugate, Units.smul_def, smul_smul, h.val_inv_mul, one_smul]
@@ -589,7 +585,6 @@ theorem inv_inv_inv (A : Matrix n n α) : A⁻¹⁻¹⁻¹ = A⁻¹ := by
   · simp [nonsing_inv_apply_not_isUnit _ h]
 #align matrix.inv_inv_inv Matrix.inv_inv_inv
 
-set_option synthInstance.etaExperiment true in
 theorem mul_inv_rev (A B : Matrix n n α) : (A ⬝ B)⁻¹ = B⁻¹ ⬝ A⁻¹ := by
   simp only [inv_def]
   rw [Matrix.smul_mul, Matrix.mul_smul, smul_smul, det_mul, adjugate_mul_distrib,
@@ -604,7 +599,6 @@ theorem list_prod_inv_reverse : ∀ l : List (Matrix n n α), l.prod⁻¹ = (l.r
       Matrix.mul_eq_mul, mul_inv_rev, list_prod_inv_reverse Xs]
 #align matrix.list_prod_inv_reverse Matrix.list_prod_inv_reverse
 
-set_option synthInstance.etaExperiment true in
 /-- One form of **Cramer's rule**. See `Matrix.mulVec_cramer` for a stronger form. -/
 @[simp]
 theorem det_smul_inv_mulVec_eq_cramer (A : Matrix n n α) (b : n → α) (h : IsUnit A.det) :
@@ -613,7 +607,6 @@ theorem det_smul_inv_mulVec_eq_cramer (A : Matrix n n α) (b : n → α) (h : Is
     h.mul_val_inv, one_smul]
 #align matrix.det_smul_inv_mul_vec_eq_cramer Matrix.det_smul_inv_mulVec_eq_cramer
 
-set_option synthInstance.etaExperiment true in
 /-- One form of **Cramer's rule**. See `Matrix.mulVec_cramer` for a stronger form. -/
 @[simp]
 theorem det_smul_inv_vecMul_eq_cramer_transpose (A : Matrix n n α) (b : n → α) (h : IsUnit A.det) :

This is to fix timeouts in https://github.com/leanprover-community/mathlib4/pull/3552.

See discussion at https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/!4.233552.20.28LinearAlgebra.2EMatrix.2EToLin.29.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -502,14 +502,17 @@ theorem inv_zero : (0 : Matrix n n α)⁻¹ = 0 := by
 noncomputable instance : InvOneClass (Matrix n n α) :=
   { Matrix.one, Matrix.inv with inv_one := inv_eq_left_inv (by simp) }
 
+set_option synthInstance.etaExperiment true in
 theorem inv_smul (k : α) [Invertible k] (h : IsUnit A.det) : (k • A)⁻¹ = ⅟ k • A⁻¹ :=
   inv_eq_left_inv (by simp [h, smul_smul])
 #align matrix.inv_smul Matrix.inv_smul
 
+set_option synthInstance.etaExperiment true in
 theorem inv_smul' (k : αˣ) (h : IsUnit A.det) : (k • A)⁻¹ = k⁻¹ • A⁻¹ :=
   inv_eq_left_inv (by simp [h, smul_smul])
 #align matrix.inv_smul' Matrix.inv_smul'
 
+set_option synthInstance.etaExperiment true in
 theorem inv_adjugate (A : Matrix n n α) (h : IsUnit A.det) : (adjugate A)⁻¹ = h.unit⁻¹ • A := by
   refine' inv_eq_left_inv _
   rw [smul_mul, mul_adjugate, Units.smul_def, smul_smul, h.val_inv_mul, one_smul]
@@ -586,6 +589,7 @@ theorem inv_inv_inv (A : Matrix n n α) : A⁻¹⁻¹⁻¹ = A⁻¹ := by
   · simp [nonsing_inv_apply_not_isUnit _ h]
 #align matrix.inv_inv_inv Matrix.inv_inv_inv
 
+set_option synthInstance.etaExperiment true in
 theorem mul_inv_rev (A B : Matrix n n α) : (A ⬝ B)⁻¹ = B⁻¹ ⬝ A⁻¹ := by
   simp only [inv_def]
   rw [Matrix.smul_mul, Matrix.mul_smul, smul_smul, det_mul, adjugate_mul_distrib,