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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 \[A=\left[ \begin{matrix}    3 & 4  \\    5 & 7  \\ \end{matrix} \right]\], then \[A\,(adj\,A)\]= [RPET 2002]

    A) I

    B) |A|

    C) \[|A|I\]

    D) None of these

    Correct Answer: C

    Solution :

    \[A[adj(A)]=\left[ \,\begin{matrix}    3 & 4  \\    5 & 7  \\ \end{matrix}\, \right]\,\left[ \,\begin{matrix}    7 & -4  \\    -5 & 3  \\ \end{matrix}\, \right]=\left[ \,\begin{matrix}    1 & 0  \\    0 & 1  \\ \end{matrix}\, \right]=|A|I\] \[bx+ay-z=0\].


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