Given a square matrix A, the characteristic polynomial of A is defined as PA (t) = det (tI - A), where I is the identity matrix. For example, if A = 09 H , then the characteristic polynomial of A is PA(t) = det (!I - A) = det (: (6 9) - (3 2)). and rewriting the difference as a single matrix, this becomes deta - 4 = (t- 1)(t-4) -(-2)(-3) = 1 - 5t - 2. (a) Compute the characteristic polynomial of the matrix A = b d Express your answer in the form pot* + pit + po. (b) For the polynomial in part (a), find PA' + PIA + Pol