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

  • question_answer
    For any \[2\times 2\] matrix A, if \[A(adj.\,\,A)\]= \[\left[ \begin{matrix}    10 & 0  \\    0 & 10  \\ \end{matrix} \right]\], then \[|A|\,=\] [MP PET 1999]

    A) 0

    B) 10

    C) 20

    D) 100

    Correct Answer: B

    Solution :

    \[A(adj\,.\,A)=|A|\,I\Rightarrow \,\left| \,\begin{matrix}    10 & 0  \\    0 & 10  \\ \end{matrix}\, \right|=10\,.\,\left| \,\begin{matrix}    1 & 0  \\    0 & 1  \\ \end{matrix}\, \right|\].


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