(AB+BA)

^{+}= (AB)

^{+}+(BA)

^{+}? Why does this work?

Assuming A&B are hermitian, I get why we can assume A+B is hermitian, but does it follow that A-B is hermitian? Because AB is only hermitian if AB=BA which means AB-BA=0, and I'm fairly sure 0 cannot be a hermitian operator.

Thanks