Let \(S\) denote the set of all real values of \(\lambda\) such that the system of equations \(\begin{aligned}& \lam…

Let \(S\) denote the set of all real values of \(\lambda\) 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\(\sum _{\lambda \in S}\left(|\lambda {|}^{2}+|\lambda |\right)\) is equal to

[JEE Main 2023, 1 Feb (Shift 1)]