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JEE Main & Advanced Mathematics Determinants & Matrices Question Bank Minors and Co-factors, Product of determinants

  • question_answer
    If \[\omega \] is a cube root of unity and \[\Delta =\left| \begin{matrix}    1 & 2\omega   \\    \omega  & {{\omega }^{2}}  \\ \end{matrix} \right|\], then \[{{\Delta }^{2}}\]is equal to [RPET 1984]

    A) \[-\omega \]

    B) \[\omega \]

    C) 1

    D) \[{{\omega }^{2}}\]

    Correct Answer: B

    Solution :

    Since \[\Delta ={{\omega }^{2}}-2{{\omega }^{2}}=-{{\omega }^{2}}\].  Therefore \[{{\Delta }^{2}}={{\omega }^{4}}=\omega \].


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