End MapRingMatrix.
Section ComMatrix.
(* Lemmas for matrices with coefficients in a commutative ring *)
Variable R : comRingType.
Section AssocLeft.
Variables m n p : nat.
Implicit Type A : 'M[R]_(m, n).
Implicit Type B : 'M[R]_(n, p).

Lemma trmx_mul A B : (A *m B)^T = B^T *m A^T.