Solution
= Solution
{c}
In the <finite field> $\mathbb Z_3=\{0,1,2\}$, perform ordinary addition and multiplication and then take the remainder modulo $3$. The tables are
$$
\begin{array}{c|ccc}
+&0&1&2\\\hline
0&0&1&2\\
1&1&2&0\\
2&2&0&1
\end{array}
\qquad
\begin{array}{c|ccc}
\cdot&0&1&2\\\hline
0&0&0&0\\
1&0&1&2\\
2&0&2&1
\end{array}.
$$
The nonzero elements have multiplicative inverses $1^{-1}=1$ and $2^{-1}=2$.