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?

I was looking at a problem similar to this, and these answers are great but I needed a bit more to make it click. Here is a step by step with the rules used.
$T^2 − T + I = 0$
$TT = T - I$
$TT = T - TT^{-1}$ , because $I = TT^{-1}$
$TT = IT - TT^{-1}$ , because $IT = T$
$TT = T(I-T^{-1})$ , factor out the T
$T = I - T^{-1}$ , remove T from both sides
In my case we had to prove $T^{-1} = 2I - T$ given almost the same equation (that 2 being the difference). I know this break down is probably too basic for most, but this what helped me understand how to apply those rules.
I was lead here by this duplicate.
