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

For finite-dimensional operators, use $(AB{)}^{†}=B^{†}{A}^{†}$ and the Hermitian assumptions. The commutator satisfies $[A,B{]}^{†}=-[A,B]$, soThus $i[A,B]$ is Hermitian. These adjoint identities are the intended matrix-level setting; for unbounded operators, domains and self-adjointness require additional analysis.