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?

Let $\mathbb{x}$ be any vector in the nullspace. Then $T\mathbb{x} = \mathbb{0}$. Using your equation $T^2 - T + I = 0$, what can you conclude about $\mathbb{x}$?
Alternatively if you know about minimal polynomials: How does your polynomial split?
