Answer: A
$$\underset{\begin{array}{|c|c|c|c|} \hline \text{} & \text{1}& \omega & \omega^2 \\\hline \text{1} & \text{1}& \omega & \omega^2 \\\hline \omega & \omega & \omega^2 & \text{1}\\\hline \omega^2 & \omega^2 & \text{1} & \omega\\\hline \end{array}}{\text{Cayley Table}}$$
The structure $(S,*)$ satisfies closure property, associativity and commutativity. The structure also has an identity element $(=1)$ and an inverse for each element. So, the structure is an Abelian group.