Let A, B be nX n matrices. Suppose that A is an eigenvalue of A and u is aneigenvalue of B. (The Greek letter u is pronounced "me-you".) ) Verify by giving an example, that 1 + u need not be an eigenvalue of =) Verify by givingexample, that Au need not be an eigenvalue of AB.an (c) Suppose that x is a common eigenvector of A and B such that x is an eigenvectorof A corresponding to an eigenvalue 1 of A and x is an eigenvector of B correspondingto an eigenyalue u of B. Show that 1 + u is an eigenvalue of A+ B. \text { Show that } \lambda \mu \text { is an eigenvalue of } \boldsymbol{A B} \text {. }