Let S denote the set of all real values of λ such that the system of equations λ x+y+z=1; x+λ y+z=1; x+y+λ z=1 is inconsistent, then Σ_λ ∈…

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