I'm working on this question about Latin Squares
Explain why the following Latin Square isn't the multiplication table of a group.
Here is the table:
$$\begin{array}{c|ccccc} & 1 & 2 & 3 & 4 & 5 \\ \hline 1& 1 & 2 & 3 & 4 & 5 \\ 2& 2 & 1 & 5 & 3 & 4 \\ 3& 3 & 4 & 1 & 5 & 2 \\ 4& 4 & 5 & 2 & 1 & 3 \\ 5& 5 & 3 & 4 & 2 & 1 \end{array}$$
I'm not sure how to separate the numbers further from themselves, so anyone please edit this. But as to my concern, I do not understand what's going on with this table. I cannot tell, by looking at tables, when it is or isn't a group.
Any insights?