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 *)

(* Only tall matrices have inverses. *)
Lemma mulmx1_min m n (A : 'M[R]_(m, n)) B : A *m B = 1%:M -> m <= n.