Let , where and . Let and be the identity matrix of order 2. Then, the total number…

MATHEMATICS · Subjective · CBSE · Mathematics · Matrices · Matrices

Problem

Let

z = \frac{-1 + \sqrt{3}i}{2}

, where

i = \sqrt{-1}

and

h, \delta \in \{1, 2, 3\}

. Let

P = \begin{bmatrix} (-z)^h & z^{2\delta} \\ -z^{2\delta} & z^h \end{bmatrix}

and

I

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

(h, \delta)

for which

P^2 = -I

is - - -