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KVPY Sample Paper KVPY Stream-SX Model Paper-14

  • question_answer
    If A is an \[3\times 3\] non-singular matrix such that \[AA'=A'A\]and \[B={{A}^{-\,\,1}}A',\] then BB' equals:

    A) I + B

    B) I

    C) \[B{{\,}^{-\,\,1}}\]

    D) \[({{B}^{\,-\,\,1}})'\]

    Correct Answer: B

    Solution :

    \[B={{A}^{-\,1}}A'\]\[\Rightarrow \] AB = A' \[ABB'=A'B'=(BA)'\] \[=({{A}^{-1}}A'A)=({{A}^{-1}}AA')'=A\] \[\Rightarrow \]   \[BB'=I.\]


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