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.

Lemma mul_mx_scalar m n a (A : 'M[R]_(m, n)) : A *m a%:M = a *: A.