Solution
= Solution
The <Hermitian conjugate> of a real matrix is its <transpose>, so
$$
M^\dagger=(R_1-R_1^T)^T=R_1^T-R_1=-M.
$$
Therefore $\boxed{M\text{ is anti-Hermitian for all }\theta,\phi.}$ It is also a real <skew-symmetric matrix>. It is Hermitian as well only in the exceptional case $M=0$, precisely when $R_1$ is symmetric. This includes the identity and half-turn cases from part (d), so the zero-matrix overlap should not be excluded.