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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2005

  • question_answer
    In the group \[G=\{1,3,7,9\}\] under multiplication modulo 10, the inverse of 3 is :

    A)  1                                            

    B)  3

    C)  7                                            

    D)  9

    Correct Answer: C

    Solution :

    Given \[G=\,\{1,\,\,3,\,\,7,\,\,9\}\] Here, \[1{{\times }_{10}}1=1,\,\,3{{\times }_{10}}1=3,\,\,7{{\times }_{10}}1=7\]\[9{{\times }_{10}}1=9\]. It is clear that 1 is the identity element. Since G is a group, then inverse of each element exist in G \[\Rightarrow \,\,3{{\times }_{10}}7=1=7{{\times }_{10}}3\] \[\therefore \,\,7\in G\] is the inverse of 3.


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