# Are the SDG and TDG gates hermitian?

I know that phase shift gates like $$S$$ and $$T$$ are not hermitian operators. But are the $$S^\dagger$$ and $$T^\dagger$$ gates non-hermitian too?

A matrix $$A$$ is a Hermitian if and only if
$$A = A^\dagger$$
So if $$A^\dagger$$ is Hermitian then that means $$A^\dagger = (A^\dagger)^\dagger = A$$ and so of course $$A$$ is hermitian.