proposition: Lemma mxrank_scale_nz m n a (A : 'M_(m, n)) : a != 0 -> \rank (a *: A) = \rank A.
proof: Proof. move=> nza; apply/eqP; rewrite eqn_leq -{3}[A]scale1r -(mulVf nza). by rewrite -scalerA !mxrank_scale. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype finfun bigop finset fingroup perm order) mathcomp(div prime binomial ssralg finalg zmodp matrix)