Proving Vector Space Identity: I-T Bijectivity

[Pearce_09]

Hello,
I am having trouble with particular algebra question. I don't know where to start and it would be greatly appreciated if someone could point me in the right direction.

Here is the questoin:

Let V be a vector space, where T is a linear map of V
prove if T^2 = 0 then I - T is bijective where I is the identity matrix

I tried (I-T)(I+T) = I - T^2 which equals I, but i am not sure where to go from here or if this even correct.
thanks for the time and help
regards,
adam

 

[Pearce_09]

...

 

[iNCREDiBLE]

You are done!
You just showed that $I-T$ is invertible/bijective by showing that $(I-T)(I+T) = (I+T)(I-T) = I$. Which means, by definition, $(I-T)^{-1} = (I+T)$

 

[Pearce_09]

thx for the help incredible