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If \( \omega, \omega^{2} \) are imaginary cube roots of unity and
\( \mathrm{P} \)
\( \Delta_{1}=\left|\begin{array}{ccc}1 & 1 & 1 \\ 1 & \omega & \omega^{2} \\ 1 & \omega^{2} & \omega\end{array}\right| \) and \( \Delta_{2}=\left|\begin{array}{ccc}1 & 1 & \omega \\ 1 & 1 & \omega^{2} \\ \omega^{2} & \omega & 1\end{array}\right| \), then \( \frac{\Delta_{1}}{\Delta_{2}} \)
W
is equal to
(1) \( \sqrt{3} \)
(2) \( \sqrt{3} i \)
(3) 1
(4) -1
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