>[!question] Excercise >![[Pasted image 20251027122456.png]] $\huge \begin{array}{c|ccccc} \times_{10}& 0 & 2 & 4 & 6 & 8 \\ 0 & 0 &0 & 0& 0& 0 \\ 2 &0 & 4 & 8 & 2 & 6 \\ 4 &0 & 8 & 6 & 4 & 2 \\ 6 &0 & 2 & 4 & 6 & 8 \\ 8 &0 & 6 & 2 & 8& 4 \end{array} $ The identity of this [[Algebraic Structure|Algebraic System]] is $6$ as $\forall a\in T; a\times_{10}6=a$, therefore it is a [[Monoid]]. The elemnent $0\in T$ does not have an element it can multiply with to get the identity, $6$, therefore $T$ is *not* a [[Group]].