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 detM n' (A B : 'M[R]_n'.+1) : \det (A * B) = \det A * \det B.