1. (a) Suppose U € Mnxn(C) is a unitary matrix. Show that if A is an eigenvalue of U, then |A| = 1. (b) Recall that every complex number of absolute value 1 takes the form eio for some choice of 0 E...

Extracted text: 1. (a) Suppose U € Mnxn(C) is a unitary matrix. Show that if A is an eigenvalue of U, then |A| = 1. (b) Recall that every complex number of absolute value 1 takes the form eio for some choice of 0 E [0, 27]. For every choice of real number 0 between 0 and 27, write down a non-diagonal unitary matrix U € M2x2(C) having et as an eigenvalue, and explain/justify how you came up with such a matrix.