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Let $S$ be the set of all real values of $\lambda$ such that a plane passing through the points $(-\lambda^2, 1, 1)$, $(1, -\lambda^2, 1)$ and $(1, 1, -\lambda^2)$ also passes through the point $(-1, -1, 1)$. Then $S$ is equal to:
(1) ${\sqrt{3}}$
(2) ${\sqrt{3}, -\sqrt{3}}$
(3) ${1, -1}$
(4) ${3, -3}$
BETA
