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

  • question_answer
    If \[A=\left[ \begin{align}   & 1 \\  & 2 \\  & 3 \\ \end{align} \right],\]then \[A{A}'=\] [MP PET 1992]

    A) 14

    B)   \[\left[ \begin{align}   & 1 \\  & 4 \\  & 3 \\ \end{align} \right]\]

    C)  \[\left[ \begin{matrix}    1 & 2 & 3  \\    2 & 4 & 6  \\    3 & 6 & 9  \\ \end{matrix} \right]\]

    D) None of these

    Correct Answer: C

    Solution :

    \[{A}'=[1\,\,2\,\,3]\], therefore\[A{A}'=\left[ \begin{align}   & 1 \\  & 2 \\  & 3 \\ \end{align} \right]\left[ 1\,\,2\,\,3 \right]=\left[ \begin{matrix}    1 & 2 & 3  \\    2 & 4 & 6  \\    3 & 6 & 9  \\ \end{matrix} \right]\].


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