Solution (source code)

= Solution

Using part i and $[P_\mu,P_\rho]=0$,
$$
[C_{\mu\nu},P_\rho]
=[B_\mu P_\nu-B_\nu P_\mu,P_\rho]=0.
$$
Thus
$$
\boxed{[C_{\mu\nu},P_\rho]=0}.
$$