CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2003

  • question_answer For non-singular square matrices A, B and C of the same order,\[{{(A{{B}^{-1}}C)}^{-1}}\]is equal to:

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

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

    C)  \[CB{{A}^{-1}}\]              

    D)         \[{{C}^{-1}}B{{A}^{-1}}\]

    E)  \[{{C}^{-1}}BA\]

    Correct Answer: D

    Solution :

    \[{{(A{{B}^{-1}}C)}^{-1}}\] \[={{C}^{-1}}{{({{B}^{-1}})}^{-1}}{{A}^{-1}}={{C}^{-1}}B{{A}^{-1}}\]

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