Matrices and Determinants: JEE Main 2023 Mathematics question

Let $S$ denote the set of all real values of $\lambda$ such that the system of equations $\lambda x+y+z=1$ $x+\lambda y+z=1$ $x+y+\lambda z=1$ is inconsistent, then \sum_\limits{\lambda \in S}\left(|\lambda|^{2}+|\lambda|\right) is equal to