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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 matrix \[A=\left[ \begin{matrix}    3 & 2 & 4  \\    1 & 2 & -1  \\    0 & 1 & 1  \\ \end{matrix} \right]\]and \[{{A}^{-1}}=\frac{1}{K}adj(A),\] then \[K\]is  [UPSEAT 2002]

    A) 7

    B) -7

    C) \[\frac{1}{7}\]

    D) 11

    Correct Answer: D

    Solution :

    \[K=\,|A|\]; \[|A|\,\,=\left| \,\begin{matrix}    3 & 2 & 4  \\    1 & 2 & -1  \\    0 & 1 & 1  \\ \end{matrix}\, \right|\,=\,\,11\].


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