proposition: Lemma scalar_mx_mul : forall n a b, @scalar_mx n (a * b) === a%:M *m b%:M.
proof: Proof. by move=> n a b; rewrite -> mulmx_scalar; rewrite /scalar_mx /scalemx=> i j; by case (i==j); ring. Qed.
imports: ssreflect ssrbool ssrfun eqtype ssrnat seq choice fintype finfun bigops ssralg groups perm zmodp morphisms Ring RingClass bigopsClass Setoid Morphisms