Let $V$ be an n-dimensional vector space and let $T:V\rightarrow V$ be a linear transformation such that
$$Rank\:T \leq Rank\:T^{3}$$.
Then which one of the following statements is necessarily true?
- Null space$(T)$ = Range$(T)$
- Null space$(T)$ $\cap$ Range$(T)$={$0$}
- There exists a nonzero subspace $W$ of $V$ such that Null space$(T)$ $\cap$ Range$(T)$=$W$
- Null space$(T)$ $\subseteq$ Range$(T)$