Solution:
Option(0)
To find: Value of 
Formula used: (i) 
(ii) 
We have,
On expanding the above along 
![\begin{array}{l} \Rightarrow 1\left|\begin{array}{cc} \omega^{2} & 1 \\ 1 & \omega \end{array}\right|-\omega\left|\begin{array}{cc} \omega & \omega^{2} \\ 1 & \omega \end{array}\right|+\omega^{2}\left|\begin{array}{cc} \omega & \omega^{2} \\ \omega^{2} & 1 \end{array}\right| \\ \Rightarrow\left[1\left\{\left(\omega^{2}\right)(\omega)-(1)(1)\right\}\right]-\left[\omega\left\{(\omega)(\omega)-\left(\omega^{2}\right)(1)\right\}\right]+\left[\omega^{2}\left\{(\omega) 1-\left(\omega^{2}\right)\left(\omega^{2}\right)\right\}\right] \\ \Rightarrow\left[1\left\{\omega^{3}-1\right\}\right]-\left[\omega\left\{\omega^{2}-\omega^{2}\right\}\right]+\left[\omega^{2}\left\{\omega-\omega^{4}\right\}\right] \ldots \text { (i) } \end{array}](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-d1aa8da93227b80f172a0d3114f76315_l3.png "Rendered by QuickLaTeX.com")
As
Using the above obtained value of 
![\begin{array}{l} \Rightarrow\left[1\left\{\omega^{3}-1\right\}\right]-\left[\omega\left\{\omega^{2}-\omega^{2}\right\}\right]+\left[\omega^{2}\{\omega-\omega\}\right] \\ \Rightarrow 1\left\{\omega^{3}-1\right\} \\ \Rightarrow \omega^{3}-1 \\ \Rightarrow 1-1=0 \end{array}](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-18635f1e28782f890cc14e485da88aa4_l3.png "Rendered by QuickLaTeX.com")
Mark the tick against the correct answer in the following: If 
A. 2
B. 4
C. 0
D. 
