Prove that \{0} \{0}) is not isomorphic to \{0} (the group operation in both cases is multiplication).
You can just say these groups cannot be isomorphic due to the fact that has elements of order 4, namely while there are no elements of order 4 in
everything in has order
one: (1,1)
two: (-1,1), (1,-1) and (-1,-1)
or
infinite order: everything else