Let z=−1+√3i2, where i=√−1 and r,s∈{1,2,3}. Let P=[(−z)rz2 – InterviewSolution

1.	Let z=−1+√3i2, where i=√−1 and r,s∈{1,2,3}. Let P=[(−z)rz2sz2szr] and I be the identity matrix of order 2. Then the total number of ordered pairs (r,s) for which P2=–I is
Answer» Let $z = \frac{- 1 + \sqrt{3} i}{2},$ where $i = \sqrt{- 1}$ and $r, s \in {1, 2, 3} .$ Let $P = [\begin{matrix} (- z)^{r} & z^{2 s} z^{2 s} & z^{r} \end{matrix}]$ 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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