∀ {m : Type u_2} {n : Type u_3} {α : Type v} [inst : Fintype m] [inst_1 : Fintype n] [inst_2 : AddCommMonoid α]
  [inst_3 : Mul α] (e : m ≃ n) (M : Matrix m n α), M.submatrix id ⇑e * M.transpose.submatrix (⇑e) id = M * M.transpose