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 trmx_adj n (A : 'M[R]_n) : (\adj A)^T = \adj A^T.