A note on super Koszul complex and the Berezinian

We construct the super Koszul complex of a free supercommutative $A$-module $V$ rank $p|q$ and prove that its homology is concentrated in single degree it yields an exact resolution $A$. then study dual show as well isomorphic to $\Pi^{p+q} A$, with $\Pi$ parity changing functor. Finally, we that, given automorphism $V$, induced transformation on only non-trivial class by multiplication Berezinian automorphism, thus relating this group module $V$.