proposition: Lemma unitmx_mul A B : (A *m B \in unitmx) = (A \in unitmx) && (B \in unitmx).
proof: Proof. by rewrite -unitrM -det_mulmx. 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)