(a) Show that $V_0=\{(\mathbf{v}, \mathbf{0}) \mid \mathbf{v} \in V\}$ and $W_0=\{(\mathbf{0}, \mathbf{w}) \mid \mathbf{w} \in W\}$ are complementary subspaces, as in Exercise 2.2.24, of the Cartesian product space $V \times W$, as defined in Exercise 2.1.13. (b) Prove that the diagonal $D=\{(\mathbf{v}, \mathbf{v})\}$ and the anti-diagonal $A=\{(\mathbf{v}-\mathbf{v})\}$ are complementary subspaces of $V \times V$.