# 问题：

Suppose $A$ and $B$ are Hermitian. Show that $i[A, B]$ is Hermitian.

## 解答

$(i[A, B])^{\dagger}=[i A, i B]^{\dagger}=\left[(i B)^{\dagger},(i A)^{\dagger}\right]=\left[-i B^{\dagger},-i A^{\dagger}\right]=-i[B, A]=i[A, B]$.

#### 参考

[1]www.qtumist.com