Using the rules of bra-ket algebra, prove or evaluate the following: (a) tr(XY) = tr(Y X), where X and Y are operators. (b) (XY) = Y X', where X and Y are operators. (c) explif (A)] =? in ket-bra form, where A is a Hermitian operator whose eigen- values are known. (d) Ey*, (x')ya(x"), where va (x') = (x'la')