Let $X$ be a nonempty set and $*$ operation defined on elements of $X$ such that for $a, b$ from $X$ there is $(a*b)*b=b*(b*a)=a$. Prove that operation $*$ is commutative. Exercise is taken from the "Introduction to algebra" by Kostrikin.
2026-02-23 06:38:10.1771828690
Operation satysfaying b*(b*a)=a=(a*b)*b for all a and b must be commutative
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$a=(a(ba))(ba)=(ba)((ba)a)=(ba)b$.
Thus, $ab=((ba)b)b=ba$