show that if f is in Hom(U,U) such that f^{2}=f then V= ker f + ker(f - id_{v}). also let B_{0 }be an ordered basis For ker f and B1 be ordered basis for ker(f-idv). if B is an ordered basis and B=B_{0}+ B_{1}for V. what is the matrix representation of f given B,B?