Prove that the [[Set|set]] $\set{1,2,3,4}$ is a [[Group]] under $\times_5$. $\huge \begin{array}{c|cccc} \times_{5} & 1 & 2 & 3 & 4 \\ \hline 1& 1 & 2 & 3 & 4\\ 2& 2 & 4 & 1 & 3 \\ 3& 3 & 1 & 4 & 2 \\ 4& 4 & 3 & 2 & 1 \\ \end{array} $ This set under the operation satisfies - Associativitiy (lemma. multiplication) - The identity is 1 - $\times_5$ is closed under the set - The inverse