proposition: Lemma mulmx1_unit A B : A *m B = 1%:M -> A \in unitmx /\ B \in unitmx.
proof: Proof. by move=> AB1; apply/andP; rewrite -unitmx_mul AB1 unitmx1. 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)