Exercise
Let m be a natural number greater than 1. For which values of m is the map Z/mZ -> Z/mZ given by x -> x2 a morphism?
None
m = 2
All even m
All m
No, try m = 2.
Yes.
Part of the check is that the map respects addition. This works out well because the cross product term in (a + b)2 is 0 mod m.
No. The map respects addition if, for all a, b, the cross product term in
(a + b)2 is 0 mod m.
No. It looks like you have made a wild guess.