If \[1,\omega ,{{\omega }^{2}}\] are the cube roots of unity, then\[\Delta =\left| \,\begin{matrix} 1\,\,\,\, & {{\omega }^{n}} & {{\omega }^{2n}} \\ {{\omega }^{n}}\,\, & \,\,\,{{\omega }^{2n}}\,\, & 1 \\ {{\omega }^{2n}}\, & 1\,\, & {{\omega }^{n}} \\ \end{matrix} \right|\]= [AIEEE 2003]

If \[1,\omega ,{{\omega }^{2}}\] are the cube roots of unity, then\[\D

1.	If \[1,\omega ,{{\omega }^{2}}\] are the cube roots of unity, then\[\Delta =\left\| \,\begin{matrix} 1\,\,\,\, & {{\omega }^{n}} & {{\omega }^{2n}} \\ {{\omega }^{n}}\,\, & \,\,\,{{\omega }^{2n}}\,\, & 1 \\ {{\omega }^{2n}}\, & 1\,\, & {{\omega }^{n}} \\ \end{matrix} \right\|\]= [AIEEE 2003]
A.	0
B.	1
C.	\[\omega \]
D.	\[{{\omega }^{2}}\]
Answer» B. 1

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If \[1,\omega ,{{\omega }^{2}}\] are the cube roots of unity, then\[\Delta =\left| \,\begin{matrix} 1\,\,\,\, & {{\omega }^{n}} & {{\omega }^{2n}} \\ {{\omega }^{n}}\,\, & \,\,\,{{\omega }^{2n}}\,\, & 1 \\ {{\omega }^{2n}}\, & 1\,\, & {{\omega }^{n}} \\ \end{matrix} \right|\]= [AIEEE 2003]

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