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 scalemxAr a A B : a *: (A *m B) = A *m (a *: B).
Canonical lin_mulmx_additive := Additive lin_mulmx_is_linear.