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JEE Main & Advanced Mathematics Determinants & Matrices Question Bank Special types of matrices, Transpose, Adjoint and Inverse of matrices

  • question_answer
    If \[A=\left[ \begin{matrix}    5 & 2  \\    3 & 1  \\ \end{matrix} \right],\]then \[{{A}^{-1}}\]= [EAMCET 1988]

    A) \[\left[ \begin{matrix}    1 & -2  \\    -3 & 5  \\ \end{matrix} \right]\]

    B) \[\left[ \begin{matrix}    -1 & 2  \\    3 & -5  \\ \end{matrix} \right]\]

    C) \[\left[ \begin{matrix}    -1 & -2  \\    -3 & -5  \\ \end{matrix} \right]\]

    D) \[\left[ \begin{matrix}    1 & 2  \\    3 & 5  \\ \end{matrix} \right]\]

    Correct Answer: B

    Solution :

    Since\[\left[ \begin{matrix}    5 & 2  \\    3 & 1  \\ \end{matrix} \right]\,\left[ \begin{matrix}    -1 & 2  \\    3 & -5  \\ \end{matrix} \right]\,=\left[ \begin{matrix}    1 & 0  \\    0 & 1  \\ \end{matrix} \right]\].


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