I am using Charles Pinter's book on abstract algebra . I have to prove that
for any finite group G, if we define the set
i.e. set of elements in G which are not equal to its own inverse. I have to prove that
set S has even no of elements. Now I can see that if some x is in S then its inverse
has to be there since
so members of S appear in pairs. So I can see that , its cardinality has to be even.
But how can I prove this ? any hints ?