(a) Show that V0 = ( (v, 0) | v V ) and w0 = (...

Question:

(a) Show that V0 = ( (v, 0) | v ∈ V ) and w0 = ( (0, w) | w e w ) are complementary subspaces, as in Exercise 2.2.24, of the Cartesian product space V × W, as defined in Exercise 2.1.13.
(b) Prove that the diagonal D = {(v. v)) and the amidiagonal A = {(v, -v)) are complementary subspaces of V × V.