Question 187
Suppose $S$ is a finite set with a binary operation $\star$ - that is, for any elements $a, b$ of $S$, there is defined an element $a \star b$ of $S$. It is given that $(a \star b) \star(a \star b)=b \star a$ for all $a, b \in S$.
Prove that $a \star b=b \star a$ for all $a, b \in S$.
Prove that $a \star b=b \star a$ for all $a, b \in S$.