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JEE Advanced 2016
Paper-1 2016
Question
Let $z=\frac{-1+\sqrt{3} i}{2}$, where $i=\sqrt{-1}$, and $r, s \in[1,2,3]$. Let $P=\left[\begin{array}{cc}(-z)^r & z^{2 s} \\ z^{2 s} & z^r\end{array}\right]$ and $I$ be the identity matrix of order 2 . Then the total number of ordered pairs $(r, s)$ for which $P^2=-I$ is
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