Definition copid_mx {n} r : 'M_n := 1%:M - pid_mx r.

Lemma mul_row_col m n1 n2 p (Al : 'M_(m, n1)) (Ar : 'M_(m, n2)) (Bu : 'M_(n1, p)) (Bd : 'M_(n2, p)) : row_mx Al Ar *m col_mx Bu Bd = Al *m Bu + Ar *m Bd.