JEE Main & Advanced AIEEE Solved Paper-2006

  • question_answer
    If A and B are square matrices of size\[n\times n\]such that\[{{A}^{2}}-{{B}^{2}}=(A-B)(A+B),\]then which of the following will be always true?     AIEEE  Solved  Paper-2006

    A) \[AB=BA\]

    B) Either of A or B is a zero matrix

    C) Either of A or B is an identity matrix

    D) \[A=B\]

    Correct Answer: A

    Solution :

    Given, \[{{A}^{2}}-{{B}^{2}}=(A-B)(A+8)\] \[\Rightarrow \]\[{{A}^{2}}-{{B}^{2}}={{A}^{2}}-{{B}^{2}}+AB-BA\] \[\Rightarrow \]\[AB=BA\]

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