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JEE Main & Advanced Mathematics Determinants & Matrices Question Bank Self Evaluation Test - Matrices

  • question_answer
    If \[B=\left[ \begin{matrix}    3 & 4  \\    2 & 3  \\ \end{matrix} \right]\] and \[C=\left[ \begin{matrix}    3 & -4  \\    -2 & 3  \\ \end{matrix} \right]\] and \[X=BC\],find \[{{X}^{n}}\]

    A) 0

    B) I

    C) 2I

    D) None of these

    Correct Answer: B

    Solution :

    [b] \[X=BC=\left[ \begin{matrix}    3 & 4  \\    2 & 3  \\ \end{matrix} \right]\left[ \begin{matrix}    3 & -4  \\    -2 & 3  \\ \end{matrix} \right]\] \[\Rightarrow X=BC=\left[ \begin{matrix}    1 & 0  \\    0 & 1  \\ \end{matrix} \right]=ISo\,\,{{X}^{n}}={{I}^{n}}=I\]


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