Let $\displaystyle V$ be a vector, and let $\displaystyle T:V \rightarrow V$ be linear. Prove that $\displaystyle T^2 = T_0 \iff R(T) \subseteq N(T)$. I just need a hint to get me started.

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- Feb 27th 2008, 10:52 PMlllllcomposition of linear transformation question
Let $\displaystyle V$ be a vector, and let $\displaystyle T:V \rightarrow V$ be linear. Prove that $\displaystyle T^2 = T_0 \iff R(T) \subseteq N(T)$. I just need a hint to get me started.