Past exam of the mathematical methods I course of the University of Oxford / 2019 resit / 11 / a / ii / Solution

The commutator is anti-Hermitian: $[A,B{]}^{†}=-[A,B]$. It is also Hermitian precisely when it is zero, so it is not Hermitian in general; it is Hermitian if and only if $A$ and $B$ commute. For example, $[{\sigma }_x,{\sigma }_y]=2i{\sigma }_z\ne 0$ for the Pauli matrices.