Problem 5. (a) Prove that if 2,11; E C, then = 21?: and z + w = 2 + {E ( [ ) Prove that if A E AMMALC} and 1: E C": then E = 315' Suppose A E C is an eigenvalue of A E -fnxnIZR). Show that it is also an eigenvalue of A. ( ) Suppose z E C" is an eigenveetor of A E -fnx{R). Show that 2 E C\" is also an eigenvecter A. (e) Now, assume a = 2. Assume A E M'gx) has an eigenvalue (1 + it) E (C with 5 7E D. Show that A is similar to the matrix I) a: _ (a a. J - b c d