For every $a, b$ belongs to $G$ $a*b=ab/2$ I have to find out whether $(G, *)$ is an abelian group or not I have gone up to identity but stuck at inverse please someone help
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The identity element is $2$ and the inverse of an element is $\frac{4}{a}$ – Yeipi Apr 26 '20 at 18:27
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How it is 4/a can u explain it – tarun8572 Apr 26 '20 at 18:29
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Yeipi Please do not answer in comments. Also, the inverse of an element is dependent on the element. Not every element a, b, c, d, ... $\in G$ has the inverse $\frac 4a$. – amWhy Apr 26 '20 at 18:31
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The inverse of an element $a\in G$ is $\frac{4}{a}$, which is to say $a^{-1}=\frac{4}{a}$. The reason why is because $a*b=2\Leftrightarrow \frac{ab}{2}=2\Leftrightarrow b=\frac{4}{a}$. The clue is to look that the identity element is $2$ and just find which circumstances imply $ab=2$.
Yeipi
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