This is problem 3.26 in Griffiths' Introduction to Quantum Mechanics (second editition):
An anti-hermitian (or skew-hermitian) operator is equal to minus its hemitian conjugate:
(a) Show that the expectation value of an anti-hermitian operator is imaginary.
(b) Show that the commutator of two hermitian operators is anti-hermitian. How about the commutator of two anti-hermitian operators?
For a hermitian operator, A* = A
and for an anti hermitian one, A* = -A
I used "* " for DAGGER
first I will show u that the expectation value of hermitian operator is real
<psi|A|psi>* = <psi|A|psi> = <A>, the expectation value of ...
The answer with good explanations.