I can do i) but just a bit stuck on ii).
my working for i) is: E^2-E=0 so that means is an eigenvalue of E^2-E=0, since the zero vector only has an eigenvalue of 0, then and so \lambda = 0 or 1
I sorta have an idea but dono how to finish this Q
If we let x be a eigenvector of corresponding to , then we have
Now just playing around:
but dono how to get to the result