If \[\omega \] is an imaginary root of unity, then the value of \[\left| \,\begin{matrix} a & b{{\omega }^{2}} & a\omega \\ b\omega & c & b{{\omega }^{2}} \\ c{{\omega }^{2}} & a\omega & c \\ \end{matrix}\, \right|\] is [MP PET 2004]

\[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}\]

\[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}-3abc\]

If \[\omega \] is an imaginary root of unity, then the value of \[\lef

1.	If \[\omega \] is an imaginary root of unity, then the value of \[\left\| \,\begin{matrix} a & b{{\omega }^{2}} & a\omega \\ b\omega & c & b{{\omega }^{2}} \\ c{{\omega }^{2}} & a\omega & c \\ \end{matrix}\, \right\|\] is [MP PET 2004]
A.	\[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}-3abc\]
B.	\[{{a}^{2}}b-{{b}^{2}}c\]
C.	0
D.	\[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}\]
Answer» D. \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}\]

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If \[\omega \] is an imaginary root of unity, then the value of \[\left| \,\begin{matrix} a & b{{\omega }^{2}} & a\omega \\ b\omega & c & b{{\omega }^{2}} \\ c{{\omega }^{2}} & a\omega & c \\ \end{matrix}\, \right|\] is [MP PET 2004]

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