linear operator on a vector space V such that $T^2 -T +I=0$ let T be a linear operator on a vector space V such that $T^2 -T +I=0$.Then


*

*T is oneone but not onto.

*T is onto but not one one.

*T is invertible.

*no such T exists.


could any one give me just hint?

$$
T^2-T+I=0 \iff T(I-T)=I=(I-T)T,
$$
i.e. $T$ is invertible and $T^{-1}=I-T$. In particular $T$ is injective and surjective.
