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RAJASTHAN ­ PET Rajasthan PET Solved Paper-2012

  • question_answer
    If A and B are square matrices of size\[n\times n\]such that\[{{A}^{2}}-{{B}^{2}}=(A\text{ }B)(A+B)\]then which of the following will be always true?

    A)  \[AB=BA\]

    B)  Either\[A=O\]or\[B=O\]

    C)  Either\[A=I\]or\[B=I\]

    D)  \[A=B\]

    Correct Answer: A

    Solution :

    Given, \[{{A}^{2}}-{{B}^{2}}=(A-B)(A+B)\] \[\Rightarrow \] \[{{A}^{2}}-{{B}^{2}}={{A}^{2}}+AB-BA-{{B}^{2}}\] \[\therefore \]Above relation will hold always, if\[AB=BA\].


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