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 det_ublock n1 n2 Aul (Aur : 'M[R]_(n1, n2)) Adr :
\det (block_mx Aul Aur 0 Adr) = \det Aul * \det Adr.