A) abelian
B) finite
C) infinite
D) None of these
Correct Answer: A
Solution :
\[{{(a*b)}^{2}}=(a*b)*(b*b)\]for all\[a,\,\,b\in G\] \[\Rightarrow \]\[(a*b)*(a*b)=(a*a)*(b*b)\]for all\[a,\,\,b\in G\] \[a*(b*a)*b=a*((a*b)*b\] for all\[a,\,\,b\in G\] \[\Rightarrow \]\[b*a=a*b\]for all\[a,\,\,b\in G\] {by cancellation laws} \[\Rightarrow \,\,\,G\]is abelian.You need to login to perform this action.
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