linear homework

Hi this is due on tuesday and i need a little help.

let V and W be vector spaces such that dim(V) = dim(W), and let T:V->W be a linear transformation. prove that there exists bases beta and alpha for V and W respectively, such that linear transform ([T] beta alpha) is a diagonal matrix.(hint: begin with a basis for N(T) and extend it for a basis for V)

thank you