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JEE Main & Advanced Mathematics Determinants & Matrices Question Bank Types of matrices, Algebra of matrices

  • question_answer
    If \[P=\left( \begin{matrix}    i & 0 & -i  \\    0 & -i & i  \\    -i & i & 0  \\ \end{matrix} \right)\] and \[Q=\left( \begin{matrix}    -i & i  \\    0 & 0  \\    i & -i  \\ \end{matrix} \right)\],then \[PQ\] is equal to [Kerala (Engg.) 2002]

    A) \[\left( \begin{matrix}    -2 & 2  \\    1 & -1  \\    1 & -1  \\ \end{matrix} \right)\]

    B) \[\left( \begin{matrix}    \,2 & -2  \\    -1 & \,\,\,1  \\    -1 & \,\,\,1  \\ \end{matrix} \right)\]

    C) \[\left( \begin{matrix}    2 & -2  \\    -1 & \,\,1  \\ \end{matrix} \right)\]

    D) \[\left( \begin{matrix}    1 & 0 & 0  \\    0 & 1 & 0  \\    0 & 0 & 1  \\ \end{matrix} \right)\]

    Correct Answer: B

    Solution :

    First note that PQ must be of order 3 × 2 and its (1, 1)th entry is \[i(-i)+0-i(i)=2\].


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