In https://www.physics.uci.edu/~tanedo/files/notes/SUSYXD.pdf, on page 47, I found that for ${\cal N}=2$ SUSY (massless representation), we start with a state $|\Omega\rangle$ with helicity $\lambda_0=0$ and then apply the SUSY generators, we have 2 states $$a_1^\dagger|\Omega\rangle; \ \ \ a_2^\dagger|\Omega\rangle $$ Both of the above states are having helicities $\lambda=\lambda_0+1/2=1/2$. Then according to the notes we have $$a_2^\dagger a_1^\dagger|\Omega\rangle= a_1^\dagger a_2^\dagger|\Omega\rangle=|\text{State with }\lambda=1\rangle$$
I do not understand equality in the above expression, since the SUSY generators are fermionic in nature, should not $a_1^\dagger a_2^\dagger=-a_2^\dagger a_1^\dagger$?
