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 diag_mxC n (d e : 'rV[R]_n) :
diag_mx d *m diag_mx e = diag_mx e *m diag_mx d.