A) \[3\sqrt{3}i\]
B) \[-3\sqrt{3}i\]
C) \[i\sqrt{3}\]
D) 3
Correct Answer: A
Solution :
\[\left| \,\begin{matrix} 1 & 1 & 1 \\ 1 & {{\omega }^{2}} & \omega \\ 1 & \omega & {{\omega }^{2}} \\ \end{matrix}\, \right|\,=3(\omega -{{\omega }^{2}})\] \[=3\,\left[ \frac{-1+\sqrt{3}i}{2}-\frac{-1-\sqrt{3}i}{2} \right]=3\sqrt{3}\,i\].
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