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JEE Main & Advanced Mathematics Determinants & Matrices Question Bank Types of matrices, Algebra of matrices

  • question_answer
    If \[A=\left[ \begin{matrix}    1 & -2 & 1  \\    2 & 1 & 3  \\ \end{matrix} \right]\] and \[B=\left[ \begin{matrix}    2 & 1  \\    3 & 2  \\    1 & 1  \\ \end{matrix} \right]\], then \[{{(AB)}^{T}}=\] [RPET 1996]

    A) \[\left[ \begin{matrix}    -3 & -2  \\    10 & 7  \\ \end{matrix} \right]\]

    B) \[\left[ \begin{matrix}    -3 & 10  \\    -2 & 7  \\ \end{matrix} \right]\]

    C) \[\left[ \begin{matrix}    -3 & 10  \\    7 & -2  \\ \end{matrix} \right]\]

    D) \[\left[ \begin{matrix}    3 & 10  \\    2 & 7  \\ \end{matrix} \right]\]

    Correct Answer: B

    Solution :

    \[AB=\left[ \begin{matrix}    1 & -2 & 1  \\    2 & 1 & 3  \\ \end{matrix} \right]\left[ \begin{matrix}    2 & 1  \\    3 & 2  \\    1 & 1  \\ \end{matrix} \right]\] \[AB=\left[ \begin{matrix}    -3 & -2  \\    10 & 7  \\ \end{matrix} \right]\Rightarrow {{(AB)}^{T}}=\left[ \begin{matrix}    -3 & 10  \\    -2 & 7  \\ \end{matrix} \right]\].


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