Consider some integral domain $D$ and $a \in D$. If $a$ is reducible, then does it imply that $a$ is not a unit?
Contraposition of this statement is "if $a$ is unit, then $a$ is irreducible", which in my opinion is not true, because an irreducible element is by definition a non-unit. However, I'm struggling to find some simple counter example to this statement, i. e. find some integral domain $D$ where $a$ is reducible and unit at the same time.
Any hints on this would be much appreciated, thank you in advance.