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 *)

Lemma adj1 n : \adj (1%:M) = 1%:M :> 'M[R]_n.