proposition: Lemma tr_perm_mx n (s : 'S_n) : (perm_mx s)^T = perm_mx s^-1.
proof: Proof. by rewrite -[_^T]mulmx1 tr_row_perm mul_col_perm trmx1 mul1mx. 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)