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

  • question_answer
    If \[X=\left[ \begin{matrix}    -x & -y  \\    z & t  \\ \end{matrix} \right]\] then transpose of adj X is  [J & K 2005]

    A) \[\left[ \begin{matrix}    t & z  \\    -y & -x  \\ \end{matrix} \right]\]

    B) \[\left[ \begin{matrix}    t & y  \\    -z & -x  \\ \end{matrix} \right]\]

    C) \[\left[ \begin{matrix}    t & -z  \\    y & -x  \\ \end{matrix} \right]\]

    D) None of these

    Correct Answer: C

    Solution :

    \[X=\left[ \begin{matrix}    -x & -y  \\    z & t  \\ \end{matrix} \right]\,\,;\,\,adj\,\,X=\left[ \begin{matrix}    t & y  \\    -z & -x  \\ \end{matrix} \right]\] \ Transpose of (adj (X)) = \[\left[ \begin{matrix}    t & -z  \\    y & -x  \\ \end{matrix} \right]\].


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