Suppose $I$ is an $n \times n$ identity matrix, and $S$ is the $n \times n$ symmetric matrix with rank equals two. I was reading something saying that: $$\det(I-S)=(1-\lambda_1)(1-\lambda_2)$$
where $\lambda_1$ and $\lambda_2$ are the two largest (in absolute values) eigenvalues of $S$. Can anyone provide some clues for proving this? Thanks in advance!