Prove each, assuming that the operations are defined, where G, H, and J are matrices, where Z is the zero matrix, and where r and s are scalars.
(a) Matrix addition is commutative G + H = H + G.
(b) Matrix addition is associative G + (H + J) = (G + H) + J.
(c) The zero matrix is an additive identity G + Z = G.
(d) 0 ∙ G = Z
(e) (r + s)G = rG + sG
(f) Matrices have an additive inverse G + (- 1) ∙ G = Z.
(g) r(G + H) = rG + rH
(h) (rs)G = r(sG)