Suppose A is a 3 x 3 real symmetric matrix with three eigenvalues: 1,2,-2. The vector V1 = (1, -2, 1)T is an eigenvector of A corresponding to the eigenvalue 1. Let B = A^5 - 4A^3 + i .
(a). Show that V1 = (1, -2, 1)T is an eigenvector of B.
(b). Find all eigenvalues of B.
(c). Find B.