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J & K CET Engineering J and K - CET Engineering Solved Paper-2008

  • question_answer
    If A is a square matrix. A' its transpose, then \[\frac{1}{2}(A-A')\]is

    A)  a symmetric matrix

    B)  a skew symmetric matrix

    C)  a unit matrix

    D)  an elementary matrix

    Correct Answer: B

    Solution :

    Now, \[{{\left[ \frac{1}{2}\,(A-A') \right]}^{'}}=\frac{1}{2}(A-A')'\] \[=\frac{1}{2}(A'-A)\] \[=-\frac{1}{2}(A-A')\] Hence, it is a skew symmetric matrix.


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