Invertibility of linear combinations of two idempotents

Let $P$ and $Q$ be two idempotents on a Hilbert space. In this note, we prove that the invertibility of the linear combination $\lambda_1P+\lambda_2Q$ is independent of the choice of $\lambda _i$, $i=1,2,$ if $\lambda_1\lambda_2\neq 0$ and $\lambda_1+\lambda_2\neq 0.$