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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2011

  • question_answer
    If A and B are symmetric matrices of the same order, then which one of the following is not true?

    A)  A + B is symmetric

    B)  A - B is symmetric

    C)  AB + BA is symmetric

    D)  AB - BA is symmetric

    Correct Answer: D

    Solution :

    Given, A and B are symmetric matrix of same order. \[\Rightarrow \]               \[A=A',\,\,B=B'\]                              ?? (i) (i) \[(A+B)'=A'+B'=A+B\] [from Eq. (i)] \[\Rightarrow \] \[(A-B)\] is symmetric. (iii) \[(AB+BA)'=(AB)'+(BA)'\]                 \[=B'A'+A'B'\]                 \[=BA+AB\]  [from Eq. (i)]                 \[=-(AB-BA)\] \[\Rightarrow \]\[(AB-BA)\] is skew - symmetric matrix.


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