1. Z/2Z x Z/2Z

hey guys, was wondering if someone could tell me what this would be represented as in a cayley table? (Z being the set of integers)
$Z/2Z \times Z/2Z$
i know that $Z/2Z = \{0,1\}$, and $(Z/2Z)^{\times} = \{0,1\}$, but i dont know what $Z/2Z \times Z/2Z$ is!!
$Z/2Z \times Z/2Z$
i know that $Z/2Z = \{0,1\}$, and $(Z/2Z)^{\times} = \{0,1\}$, but i dont know what $Z/2Z \times Z/2Z$ is!!
I assume that $Z/2Z=\mathbb{Z}/2\mathbb{Z}=\mathbb{Z}_2$. Then, $\mathbb{Z}_2\oplus\mathbb{Z}_2=\{0,1\}\times\{0,1\ }$ with addition defined by $(x,y)+(z,t)=(x+z,y+t)$. Is that what you're asking?