JEE Advanced 2016 Paper 1 Mathematics Q18

Mathematics

Problem

Let

z=\frac{-1+\sqrt3i}{2}

, where

i=\sqrt{-1}

, and

r,s\in\{1,2,3\}

. Let

P=\begin{bmatrix}(-z)^r&z^{2s}\\z^{2s}&z^r\end{bmatrix}

and

I

be the identity matrix of order 2. Then the total number of ordered pairs

(r,s)

for which

P^2=-I