A) 1
B) 0
C) \[\omega \]
D) \[{{\omega }^{2}}\]
Correct Answer: B
Solution :
\[\left| \,\begin{matrix} 1 & \omega & {{\omega }^{2}} \\ \omega & {{\omega }^{2}} & 1 \\ {{\omega }^{2}} & 1 & \omega \\ \end{matrix}\, \right|=\left| \,\begin{matrix} 1+\omega +{{\omega }^{2}} & \omega & {{\omega }^{2}} \\ 1+\omega +{{\omega }^{2}} & {{\omega }^{2}} & 1 \\ 1+\omega +{{\omega }^{2}} & 1 & \omega \\ \end{matrix}\, \right|\] \[=\,\left| \,\begin{matrix} 0 & \omega & {{\omega }^{2}} \\ 0 & {{\omega }^{2}} & 1 \\ 0 & 1 & \omega \\ \end{matrix}\, \right|=0\].
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