proposition: Lemma conj_mx_irr : mx_irreducible rGB <-> mx_irreducible rG.
proof: Proof. have Bfree: row_free B by rewrite row_free_unit. split => /mx_irrP[n_gt0 irrG]; apply/mx_irrP; split=> // U. rewrite -[U](mulmxKV uB) -mxmodule_conj -mxrank_eq0 /row_full mxrankMfree //. by rewrite mxrank_eq0; apply: irrG. rewrite -mxrank_eq0 /row_full -(mxrankMfree _ Bfree) mxmodule_conj mxrank_eq0. exact: irrG. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path) mathcomp(div choice fintype tuple finfun bigop prime) mathcomp(ssralg poly polydiv finset fingroup morphism) mathcomp(perm automorphism quotient finalg action zmodp) mathcomp(commutator cyclic center pgroup matrix mxalgebra) mathcomp(mxpoly)