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JEE Advanced 2016 Paper 1 Mathematics Question 54

Let \(z = \displaystyle\frac{-1 + \sqrt{3}i}{2}\) where \(i = \sqrt{-1}\), and \(r, s \in \{1,2,3\}\). Let \(P = \left[ \begin{array}{cc} (-z)^r & z^{2s} \\ z^{2s} & z^r \end{array} \right]\) 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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