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I am confused with an example I found, which says that for a given graded vector space $V$ such that $V^0=0$ and $V^1=0$, then $(\bigwedge V)^2=\bigwedge^2V =V^2$.

Two questions:

1.$V^0$ is not the ground field, right?But then what is it?

2.Why this is true and how is this justified?

Thanks!

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