Question 1 - A-Level Maths

$$x ^ { * } y \equiv x + y - 2 x y ( \bmod 4 )$$

Complete the Cayley table below.
* 0 1 2 3
0
1
2
3
Show that $G$ is a group under the operation *
(You may assume the associative law is satisfied.)
State the order of each element of $G$.
State whether $G$ is a cyclic group, giving a reason for your answer.