Suppose V is a real vector space of finite dimension n. Call the set of matrices from V into itself M(V). Let T be in M(V). Consider the two subspaces U = {X ∈ M(V) : TX = XT} and W = {TX − XT : X ∈ M(V)}. Which of the following must be TRUE?
I. If V has a basis containing only eigenvectors of T then U = M(V).
II. dim (U) + dim (W) = n^2
III. dim (U) < n
(A)I only (B)II only (C)III only (D)I and II only
B