Consider the set of numbers $\displaystyle a + bi$ where $\displaystyle a$ and $\displaystyle b$ are elements of $\displaystyle \mathbb{Z}/2\mathbb{Z}$. $\displaystyle i^2 = -1$ which in $\displaystyle \mathbb{Z}/2\mathbb{Z}$ is the same as $\displaystyle 1$. Write down all 4 elements of this set of numbers. Which elements have inverses?