Section MatrixAlgType.
Variable n' : nat.
Local Notation n := n'.+1.
Canonical matrix_algType :=
Eval hnf in AlgType R 'M[R]_n (fun k => scalemxAr k).
End MatrixAlgType.
(* The theory of determinants *)

Lemma is_perm_mxV (A : 'M_n) : is_perm_mx A^-1 = is_perm_mx A.