proposition: Lemma det_inv A : \det (invmx A) = (\det A)^-1.
proof: Proof. case uA: (A \in unitmx); last by rewrite /invmx uA invr_out ?negbT. by apply: (mulrI uA); rewrite -det_mulmx mulmxV ?divrr ?det1. 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)