proposition: Lemma eqmx_scale m n a (A : 'M_(m, n)) : a != 0 -> (a *: A :=: A)%MS.
proof: Proof. move=> nz_a; apply/eqmxP; rewrite scalemx_sub //. by rewrite -{1}[A]scale1r -(mulVf nz_a) -scalerA scalemx_sub. 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)