Question: Let $\displaystyle W$ be a subspace of vector space $\displaystyle V$ and that $\displaystyle T: V \rightarrow V$ is linear. Prove that subspaces $\displaystyle \{0\},V,R(T),N(T)$ are all T-invariant.

I feel that the trick is really simple but I just cannot grasp it. Any pointers would be appreciated - thanks.