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BCECE Engineering BCECE Engineering Solved Paper-2001

  • question_answer
    If A is involutory matrix and I is unit matrix of same order, then \[(I-A)(I+A)\] is:

    A)  zero matrix       

    B)  A                           

    C) \[I\]                      

    D)         2A

    Correct Answer: A

    Solution :

    Key Idea: If A in involutory matrix, then \[{{A}^{2}}=I\]Since, A is involutory matrix. \[\therefore \]  \[{{A}^{2}}=I\]                                                   ?(i) Now,     \[(I-A)(I+A)\]                 \[={{I}^{2}}-{{A}^{2}}\] \[=I-I\]                                  [from (i)] \[=0\]


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