Finding Eigenvalues to Prove trace P is Nonnegative Integer

[dyanmcc]

I'm having trouble with this: Prove that if P is a linear map from V to V and satisfies P^2 = P, then trace P is a nonnegative integer.

I know if I find the eignevalues , their sum equals trace P. But how do I find them here?

any thoughts?

Thanks

 

[Hurkyl]

I know if I find the eignevalues , their sum equals trace P. But how do I find them here?

Start with a definition.

 

[matt grime]

P satisfies the equation X^2-X=0...