Let A and B be Hermitian matrices with AB = BA and let N = A + iB. 1) Show that N is normal. 2) Show that A = 1/2(N+N*) (* = conjugate transpose) and find a formula for B. 3) Let U be a unitary matrix such that U*NU is a diagonal matrix. Show that U*AU and U*BU is diagonal matrices. I had no problems with 1) and 2) but I simply can't figure out 3)... Please help.