Let \( \omega=-\frac{1}{2}+i \frac{\sqrt{3}}{2} \), then value of t...

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Let \( \omega=-\frac{1}{2}+i \frac{\sqrt{3}}{2} \), then value of the determinant \( \left|\begin{array}{ccc}1 & 1 & 1 \\ 1 & -1-\omega^{2} & \omega^{2} \\ 1 & \omega^{2} & \omega\end{array}\right| \) is
(a) \( 3 \omega \)
(b) \( 3 \omega(\omega-1) \)
(c) \( 3 \omega^{2} \)
(d) \( 3 \omega(1-\omega) \)
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