Past exam of the mathematics course of the University of Oxford / 2023 / Prelims / Mathematics I / 5 / a / i / Solution

In the finite field ${\mathbb{Z}}_3=\{0,1,2\}$, perform ordinary addition and multiplication and then take the remainder modulo $3$. The tables areThe nonzero elements have multiplicative inverses $1^{-1}=1$ and $2^{-1}=2$.