(-1) ^+ (i + j) * determinant (row' i (col' j A)).

(* The adjugate matrix :spose of the matrix of cofactors *)
Fact adjugate_key : unit. Proof. by []. Qed..
Notation "A *m B" := (mulmx A B) : r

(* Non-commutative transpose requires multiplication in the converse ring. *) Lemma trmx_mul_rev (R : ringType) m n p (A : 'M[R]_(m, n)) (B :