Definition matrix_ringMixin :=
  RingMixin (@mulmxA n n n n) (@mul1mx n n) (@mulmx1 n n)
            (@mulmxDl n n n) (@mulmxDr n n n) matrix_nonzero1.Canonical matrix_ringType := Eval hnf in RingType 'M[R]_n matrix_ringMixin.Canonical matrix_lAlgType := Eval hnf in LalgType R 'M[R]_n (@scalemxAl n n n).

Lemma scalar_mx_is_multiplicative : multiplicative (@scalar_mx n).