= Solution
The <commutator> of two <linear operators> is $\boxed{[A,B]=AB-BA}$. Write $T^\dagger$ for the <adjoint operator>, using the <inner product> convention linear in its second argument. Since $A^\dagger=A$ and $B^\dagger=B$,
$$
[A,B]^\dagger=B^\dagger A^\dagger-A^\dagger B^\dagger=BA-AB=-[A,B].
$$
Thus the <commutator> is anti-self-adjoint. With $C=-i[A,B]$, conjugation of the scalar gives
$$
\boxed{C^\dagger=i[A,B]^\dagger=-i[A,B]=C.}
$$
All products are understood on the stated common <operator domain>; for physical unbounded <linear operators>, the state must lie in the relevant product domains and have the finite moments used below.
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