Consider the set $S=\{1,\omega,\omega ^2\}$, where $\omega$ and $\omega^2$ are cube roots of unity. If $*$ denotes the multiplication operation, the structure $(S,*)$ forms:

A Group is an algebraic structure which satisfies
1) closure
2) Associativity
3) Have Identity element
4) Invertible
Over '*' operation the $ S$ = {$1$, $w$, $w^{2}$ } satisfies the above properties.
The identity element is $1$ and inverse of $1$ is$ 1$, inverse of$ w$ is $w^{2}$ and inverse of$ w^{2}$ is $w$