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 mulmx1_unit A B : A *m B = 1%:M -> A \in unitmx /\ B \in unitmx.