Multiple Choice Questions on Let A B C and D be n times n matrix each with non zero determinants If ABCD I then B 1 is ........ for NDA Exam Preparation

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Multiple Choice Questions

Let A B C and D be n times n matrix each with non zero determinants If ABCD I then B 1 is ........

Mathematics (NDA) Matrices and Determinants
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    Let A, B, C, and D be n × n  matrix each with non zero determinants.If ABCD =I then B-1 is?

    ABC

    Incorrect Answer

    ADC

    Incorrect Answer

    CDA

    Correct Answer

    DA-1

    Incorrect Answer
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    Explanation:

    ABCD=I

    ABCD D-1 C-1   = D-1 C-1  

    AB   = D-1 C-1  

     A-1 AB  =  A-1 D-1 C-1  

    B=  A-1 D-1 C-1

    B  -1   =  (  A-1 D-1 C-1 )  -1

    =CDA

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