(e) Let {u_1, u_2}, {v_1, v_2}, and {w_1, w_2} be bases for R^2. If X is the transition matrix corresponding to a change of basis from {u_1, u_2} to {v_1, v_2} and Y is the transition matrix corresponding to a change of basis from {v_1, v_2} to {w_1, w_2}, then Z = XY is the transition matrix corresponding to a change of basis from {u_1, u_2} to {w_1, w_2}.