Isomorphism of Groups (C.S.I.R) Suppose $(F , +, .)$ is the finite Field with $9$ elements. Let $G = (F , +)$ and $H = (F \setminus \{0\}, .)$ denotes the underlying additive and multiplicative groups respectively. Then which are TRUE ?


*

*$ G \cong \mathbb Z_3 \times \mathbb Z_3$.

*$G \cong \mathbb Z_9$.

*$ H \cong \mathbb Z_2 \times \mathbb Z_2 \times \mathbb Z_2$.

*$ G \cong \mathbb Z_3 \times \mathbb Z_3$ and  $ H \cong \mathbb Z_8$
I know that $H$ is a cyclic group and $o(G) = 3^2$,  So $G \cong \mathbb Z_9$ or $ G \cong \mathbb Z_3 \times \mathbb Z_3$. 
Please tell me about G.
Thank you

Hint: If $p$ is the characteristic of the field (I assume $F$ is a field here), then $px = 0$ for all $x\in G$.
