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Manipal Engineering Manipal Engineering Solved Paper-2013

  • question_answer
    If\[G\]is an abelian group then for all\[a,\,\,b\in G\] \[{{b}^{-1}}*\,{{a}^{-1}}\,*b*\,a\]is equal to

    A) \[a*b\]                                

    B) \[{{a}^{-1}}*{{b}^{-1}}\]

    C) \[e\]     

    D)  None of these

    Correct Answer: C

    Solution :

                                    \[{{b}^{-1}}*{{a}^{-1}}*b*a=({{b}^{-1}}*{{a}^{-1}})*(b*a)={{(a*b)}^{-1}}\] \[*(b*a)={{(a*b)}^{-1}}*(a*b)=e\]


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