P24.2. (i) Let T : V - V be a self-adjoint operator on a finite-dimensional inner product space. Assuming that 3 and 5 are the only eigenvalues of T, prove that 72 - 87 + 15 idy = 0. (ii) Exhibit real (3 x 3)-matrix A such that 3 and 5 are its only eigenvalues, but A2 - 8 A + 151 # 0. P24.3. Let V be a finite-dimensional complex inner product space and let T: V - V be a linear operator satisfying T* = -T. (i) Show that all eigenvalues of T are purely imaginary (in other words, the real part equals zero). (ii) Show that the linear operators idy +T and idy -T are invertible. (iii) Show that (idy -T) (idy +T) is an isometry