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

Lemma mul_mx_row m n p1 p2 (A : 'M_(m, n)) (Bl : 'M_(n, p1)) (Br : 'M_(n, p2)) : A *m row_mx Bl Br = row_mx (A *m Bl) (A *m Br).