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

  • question_answer
    The inverse of the matrix \[\left[ \begin{matrix}    3 & -2  \\    1 & 4  \\ \end{matrix} \right]\]is  [MP PET 1994]

    A) \[\left[ \begin{matrix}    \frac{4}{14} & \frac{2}{14}  \\    \frac{-1}{14} & \frac{3}{14}  \\ \end{matrix} \right]\]

    B) \[\left[ \begin{matrix}    \frac{3}{14} & \frac{-2}{14}  \\    \frac{1}{14} & \frac{4}{14}  \\ \end{matrix} \right]\]

    C) \[\left[ \begin{matrix}    \frac{4}{14} & \frac{-2}{14}  \\    \frac{1}{14} & \frac{3}{14}  \\ \end{matrix} \right]\]

    D) \[\left[ \begin{matrix}    \frac{3}{14} & \frac{2}{14}  \\    \frac{1}{14} & \frac{4}{14}  \\ \end{matrix} \right]\]

    Correct Answer: A

    Solution :

    Let \[A=\left[ \begin{matrix}    3 & -2  \\    1 & 4  \\ \end{matrix} \right]\,\Rightarrow |A|=14\] \[\therefore \] \[adj\,A=\left[ \begin{matrix}    4 & 2  \\    -1 & 3  \\ \end{matrix} \right]\] \[\Rightarrow \] \[{{A}^{-1}}=\left[ \begin{matrix}    \frac{4}{14} & \frac{2}{14}  \\    \frac{-1}{14} & \frac{3}{14}  \\ \end{matrix} \right]\].


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