I did the hard part in (a). You should be able to do this now.(b) Deduce that , the set of non-zero elements of , is a group under multiplication mod .
Just show there exists an element that does not have an inverse. Hint: if is not prime then there exists such that , and argue that no such can be found such that .(c) Show that if is not prime, then is not a multiplicative group.
Yes.(d) Is cyclic?