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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2007

  • question_answer
    In the group \[(G,\,\,{{\otimes }_{15}}),\] where \[G=\{3,6,9,12\},\]\[{{\otimes }_{15}}\]is multiplication modulo 15, the identity element is

    A)  \[3\]                                    

    B)  \[6\]

    C)  \[12\]                                  

    D)  \[9\]

    Correct Answer: B

    Solution :

    Given,  \[G=\{3,6,9,12\}\] The composition table is
    \[{{x}_{5}}\] \[3\] \[6\] \[9\] \[12\]
    \[3\] \[9\] \[3\] \[12\] \[6\]
    \[6\] \[3\] \[6\] \[9\] \[12\]
    \[9\] \[12\] \[9\] \[6\] \[3\]
    \[12\] \[6\] \[12\] \[3\] \[9\]
    From the table 6 is the identity element.


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