A) \[{{(1-\omega )}^{2}}\]
B) 3
C) \[-3\]
D) zero
Correct Answer: B
Solution :
We have \[\left| \begin{matrix} 1 & {{\omega }^{2}} & {{\omega }^{5}} \\ {{\omega }^{3}} & 1 & {{\omega }^{4}} \\ {{\omega }^{5}} & {{\omega }^{4}} & 1 \\ \end{matrix} \right|=\left| \begin{matrix} 1 & 1 & {{\omega }^{2}} \\ 1 & 1 & {{\omega }^{2}} \\ {{\omega }^{2}} & \omega & 1 \\ \end{matrix} \right|\] \[=2{{\omega }^{3}}-{{\omega }^{2}}-{{\omega }^{4}}=2-{{\omega }^{2}}-\omega \] \[=2-(\omega +{{\omega }^{2}})\] \[=2-(-1)=3\]You need to login to perform this action.
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