Solution
= Solution
For the Grassmann-odd ghost $c$, the <BRST transformation>[BRST transformations] are
$$
QA_\mu=D_\mu c=\partial_\mu c-ig[A_\mu,c],
\qquad
Q\phi=ig[c,\phi],
\qquad
Qc=igc^2,
$$
up to a simultaneous convention-dependent sign for $Q$ and $c$. The ghost transformation makes the <BRST charge> nilpotent: $Q^2A_\mu=Q^2\phi=0$.