In Artin, Algebra, the author says that it is usually clear in a given example of a group action that the axioms for it hold. The simplest example given is the action of the group $\{1,r\}$ on $\mathbb{C}$ given by $rz = \bar{z}$.
The identity axiom for a group action is trivial. However, to verify associativity, I don't see an easier way than brute force.
In this case the only non-trivial element is $r$ so since identity function commutes with any other, we only need to check 3 cases. It still feels like a lot of work for something that should be clear. Is there an easier way?