Let P and Q be two idempotents, we review the results about the equivalence between the invertibility of a linear combination aP +bQ and that of P +Q, where a and b are any nonzero complex numbers with a + b eq 0. It is possible to extend the results to the case P and Q are square-zero elements. However, we will show that these extensions are impossible in general for P and Q being partial isometries or n-potents with n geq 3. We will show in case P and Q are square-zero elements, the invertibility of P +Q is equivalent to that of aP +bQ for nonzero a, b.