proposition: Lemma detZ n a (A : 'M[R]_n) : \det (a *: A) = a ^+ n * \det A.
proof: Proof. rewrite big_distrr /=; apply: eq_bigr => s _; rewrite mulrCA; congr (_ * _). rewrite -[n in a ^+ n]card_ord -prodr_const -big_split /=. by apply: eq_bigr=> i _; rewrite mxE. 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 countalg finalg zmodp)