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

  • question_answer
    If \[A=\left( \begin{matrix}    i & 1  \\    0 & i  \\ \end{matrix} \right)\], then \[{{A}^{4}}\]equals [AMU 1999]

    A) \[\left( \begin{matrix}    1 & -4i  \\    0 & 1  \\ \end{matrix} \right)\]

    B) \[\left( \begin{matrix}    -1 & -4i  \\    0 & -1  \\ \end{matrix} \right)\]

    C) \[\left( \begin{matrix}    -i & 4  \\    0 & i  \\ \end{matrix} \right)\]

    D) \[\left( \begin{matrix}    1 & 4  \\    0 & 1  \\ \end{matrix} \right)\]

    Correct Answer: C

    Solution :

    \[A.A=\left[ \begin{matrix}    -1 & 2i  \\    0 & -1  \\ \end{matrix} \right]\]  ,  \ \[{{A}^{4}}=\left[ \begin{matrix}    1 & -4i  \\    0 & 1  \\ \end{matrix} \right]\].


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