Solution
= Solution
The <conjugate transpose> reverses multiplication. If $A^\dagger=-A$ and $B^\dagger=-B$, then
$$
[A,B]^\dagger=B^\dagger A^\dagger-A^\dagger B^\dagger
=BA-AB=-[A,B].
$$
Thus \b[the <commutator> is again a <skew-Hermitian matrix>]. The order reversal is what produces the required minus sign.