If Aop and Bop arc Hermitian operators prove that AopBop is

If A_op and B_op arc Hermitian operators, prove that A_opB_op is Hermitian only if A_op and B_op commute.

Solution

Suppose A and B are Hermitian. Then A* = A and B* = B. If A and B commute, then (AB)* = B*A* = BA = AB. Consequently AB is Hermitian. Conversely, if AB is Hermitian, then AB = (AB)* = B*A* = BA, showing that A commutes with B