Question

Let P : V ------> V be a linear map such that P ²= P. Show that V = ker(P) + im(P) and ker(P) and im(P) ={0_V }. (For subspaces W1, W2 of V , the sum W1 + W2denotes the set of all elements of V of the form f + g with fbelongs to W₁ and g belongs to W₂. It is asubspace of V ----- you do not have to prove this.)