I am doing an exercise about tensor product.
Let $\alpha$ = $3dx+2dy+dz$ and $\beta$ = $2dx++2dy-2dz$.
What are the two-forms $\alpha \otimes \beta$, $\alpha\beta$ and $\alpha \wedge \beta$? Also, is any of them non-degenerate?
I'm stuck that I just know how to do this in matrix form. Any ideas?