[GOAL]
m : Type u_1
n : Type u_2
α : Type u_3
inst✝³ : Fintype n
inst✝² : DecidableEq n
inst✝¹ : Semiring α
A : Matrix n n α
B : Matrix n m α
inst✝ : Invertible A
⊢ ⅟A * (A * B) = B
[PROOFSTEP]
rw [← Matrix.mul_assoc, invOf_mul_self, Matrix.one_mul]
[GOAL]
m : Type u_1
n : Type u_2
α : Type u_3
inst✝³ : Fintype n
inst✝² : DecidableEq n
inst✝¹ : Semiring α
A : Matrix n n α
B : Matrix n m α
inst✝ : Invertible A
⊢ A * (⅟A * B) = B
[PROOFSTEP]
rw [← Matrix.mul_assoc, mul_invOf_self, Matrix.one_mul]
[GOAL]
m : Type u_1
n : Type u_2
α : Type u_3
inst✝³ : Fintype n
inst✝² : DecidableEq n
inst✝¹ : Semiring α
A : Matrix m n α
B : Matrix n n α
inst✝ : Invertible B
⊢ A * ⅟B * B = A
[PROOFSTEP]
rw [Matrix.mul_assoc, invOf_mul_self, Matrix.mul_one]
[GOAL]
m : Type u_1
n : Type u_2
α : Type u_3
inst✝³ : Fintype n
inst✝² : DecidableEq n
inst✝¹ : Semiring α
A : Matrix m n α
B : Matrix n n α
inst✝ : Invertible B
⊢ A * B * ⅟B = A
[PROOFSTEP]
rw [Matrix.mul_assoc, mul_invOf_self, Matrix.mul_one]
