# Degree of elements in exterior algebra

How one determines the degree of an element in the exterior algebra $$\bigwedge V$$, for a graded vector space V.

e.g.Is it true that $$\wedge^n V^2=0$$, as elements of $$V^2$$ are of degree 2?

In particular, when does the exterior product vanish? Thanks!

• I do not understand the notation, what does $V^2$ mean? – Siddharth Bhat Jul 10 at 12:09
• as $V$ is graded $V=V^0\oplus V^1\oplus V^2\oplus..$ – sasho98 Jul 10 at 12:10