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JEE Main & Advanced Sample Paper JEE Main Sample Paper-17

  • question_answer
    If \[A=\left( \begin{matrix}    1 & 1 & 1  \\    1 & {{\omega }^{2}} & \omega   \\    1 & \omega  & {{\omega }^{2}}  \\ \end{matrix} \right),\] where \[\omega \]is a complex    cube root of unity then adj. A equals

    A)  \[({{\omega }^{2}}-\omega )\bar{A}\]                  

    B) \[(\omega -{{\omega }^{2}})\bar{A}\]

    C)  \[-\bar{A}\]                                      

    D) \[\bar{A}\]

    Correct Answer: B

    Solution :

     Cofactor matrix of \[A=(\omega -{{\omega }^{2}})\left( \begin{matrix}    1 & 1 & 1  \\    1 & \omega  & {{\omega }^{2}}  \\    1 & \omega  & {{\omega }^{2}}  \\ \end{matrix} \right)\] \[=(\omega -{{\omega }^{2}})\bar{A}\]


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