Past exam of the mathematical methods I course of the University of Oxford / 2016 / 11 / a / iii / Solution

For a Hermitian matrix $H$, $H^{†}=H$. Reversing the product of $n$ identical factors has no effect, soHence every positive integer power is Hermitian. The identical-factor condition matters; a product of different Hermitian matrices need not be Hermitian.