Plese, help me to solve this:

Let T is in L(V). Put R=Im(T) and N=null(T). Note that both R and T are T-invariant. Show that R has a complementary T-invariant subspace W (i.e. V=R (direct sum) W and T(W) is included in W) if and only if R intersect N = {0}, in which case N is the unique T-invariant subspace complementary to R.

Thank you in advance!