proposition: Lemma invmx_scalar a : invmx (a%:M) = a^-1%:M.
proof: Proof. case Ua: (a%:M \in unitmx). by rewrite -scalemx1 in Ua *; rewrite invmxZ // invmx1 scalemx1. rewrite /invmx Ua; have [->|n_gt0] := posnP n; first by rewrite ![_%:M]flatmx0. by rewrite unitmxE det_scalar unitrX_pos // in Ua; rewrite invr_out ?Ua. 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)