in Yang-Mills-Theory with matter fields a dirac spinor $\psi$ transforms under BRST as $$\psi \to \delta_\Omega\psi=i\eta\psi $$ with $\eta$ being a ghost field. If I want to get the transformation of the adjoint spinor $\bar \psi$ I get by using the invariance of $\bar \psi \psi$ $$ 0=\delta_\Omega (\bar \psi\psi)=(\delta_\Omega\bar\psi)\psi - \bar\psi (\delta_\Omega\psi) \quad \Rightarrow \quad \delta_\Omega \bar\psi=i\bar\psi \eta$$ If I now want to get the transform directly, I get $$ \delta_\Omega \psi^\dagger \gamma_0=[\psi^\dagger,\Omega]_+\gamma_0=([\psi,\Omega]_+)^\dagger \gamma_0=(i\eta\psi)^\dagger\gamma_0=-i\bar\psi\eta $$ So I get different results. Where is my error? What I am not sure about, is whether if I have $(\eta\psi)^\dagger$ if this is equal to $\psi^\dagger\eta$ or $-\psi^\dagger \eta$ as the transpose part should be purely in the dirac space.
Thanks in advance.