Let $\omega$ be a nondegenerate alternating $2$-form on an $2n$-dimesional Vectorspace $V$, meaning that for all nonzero $v \in V$ the map $w \mapsto \omega(v,w)$ is not identically zero.
Why is the nth power $\omega^n = \omega \wedge \dots \wedge \omega \neq 0$?
Every textbook i have looked at says this is very easy, but i do not see it.
Thanks for your help.