I've been told that $S=${$[0],[2],[4],[6],[8]$} is a subring of $\mathbb Z_{10}$ with unity $[6]$.
How is it true though?
$[2][6]=[12]=[2]$, $[4][6]=[24]=[4]$, and so on, isn't it?
I realize I'm making a conceptual mistake somewhere. Can somebody please point it out to me?