## Find linear transformations

Find linear transformations $U,T: F^2 \rightarrow F^2$ such that $UT = T_{0}$, but $TU \neq T_{0}$. Find matrices A and B such that AB = 0 but BA is not equal to 0.

Solution.

I'm a bit confused in this problem, I'm not quite sure what I can write for U and T.