Let u, v and w be finite dimensional real vector spaces, t: u v, s:v w and p: w > u be linear transformations. if range (st) = nullspace (p)

Let U, V and W be finite dimensional real vector spaces, T: U V, S:V W and P: W > U be linear transformations. If range (ST) = nullspace (P), nullspace (ST) = range (P) and rank (T) = rank (S), then which one of the following is TRUE? (A) nullity of T= nullity ofS (B) dimension of U dimension of W (C) If dimension of V = 3, dimension of U=4, then P is not identically zero (D) If dimension of V= 4, dimension of U= 3 3 and T is one-one, then P is identically zero