Hey, I can't seem to get anywhere with this question so any help you can provide would be much appreciated.

is a linear operator on a finite dimensional vector space , whereby equals the identity operator.

1. Prove that for any given vector u in , is the vector or an eigenvector with eigenvalue

2. Prove that V is indeed the direct sum of the eigenspaces and where is considered the set of eigenvectors with eigenvalue , together with .

I am really stuck here, so thank you for any help.