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JEE Main & Advanced Mathematics Determinants & Matrices Question Bank Self Evaluation Test - Matrices

  • 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?

    A) A = B

    B) AB = BA

    C) Either of A or B is a zero matrix

    D) Either of A or B is identity matrix

    Correct Answer: B

    Solution :

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


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