prove or give a counterexample: the product of any two self adjoint operators....?

Question

the product of any two self adjoint operators on a finite dimensional inner p=roduct space is self adjoint...... No non-sense replies please, just if you know the answer or can help. thank you..

Answer 1

The product of two self-adjoint operators, one of which is also positive, is again self-adjoint if and only if the product is normal.