Q72Section C (Part C)72 of 120

Linear operators — the algebra generated by an idempotent

Let $V$ be a real vector space and $L(V)$ denote the space of linear operators on $V$ . Let $T\in L(V)$ be a non-zero operator such that $T^2=T$ . Consider the subspace $W$ of $L(V)$ spanned by $\{I,T^n:n$ is a positive integer $\}$ . Which of the following statements are necessarily true?

Multiple select: one or more options are correct. Select all of them, then submit — marks need the exact set.

Select every correct option, then submit.

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