G is a group. Suppose a in G is the unique element of order 2. Show that ax=xa for all x in G. Start by showing that xax^(-1) has order two. No idea where to start for this one.
Why is that the case?
$\displaystyle \left( {xax^{ - 1} } \right)\left( {xax^{ - 1} } \right) = ?$