If \[\omega \]is a cube root of unity, then \[\left| \,\begin{matrix} x+1 & \omega & {{\omega }^{2}} \\ \omega & x+{{\omega }^{2}} & 1 \\ {{\omega }^{2}} & 1 & x+\omega \\ \end{matrix}\, \right|=\] [MNR 1990; MP PET 1999]

If \[\omega \]is a cube root of unity, then \[\left| \,\begin{matrix}

1.	If \[\omega \]is a cube root of unity, then \[\left\| \,\begin{matrix} x+1 & \omega & {{\omega }^{2}} \\ \omega & x+{{\omega }^{2}} & 1 \\ {{\omega }^{2}} & 1 & x+\omega \\ \end{matrix}\, \right\|=\] [MNR 1990; MP PET 1999]
A.	\[{{x}^{3}}+1\]
B.	\[{{x}^{3}}+\omega \]
C.	\[{{x}^{3}}+{{\omega }^{2}}\]
D.	\[{{x}^{3}}\]
Answer» E.

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If \[\omega \]is a cube root of unity, then \[\left| \,\begin{matrix} x+1 & \omega & {{\omega }^{2}} \\ \omega & x+{{\omega }^{2}} & 1 \\ {{\omega }^{2}} & 1 & x+\omega \\ \end{matrix}\, \right|=\] [MNR 1990; MP PET 1999]

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