In $\mathbb{Z}[S_3]$, the group ring of the symmetric group on 3 elements, what is the coefficient of $e$ in $(e + (12))^2$? 
In $\mathbb{Z}[S_3]$, the group ring of the symmetric group on 3 elements, what is the coefficient of $e$ in $(e + (12))^2$?

I have $\mathbb{Z}[S_3]   = ${$a_0e + a_1(12) + a_2(13) + a_3(23) + a_4(123)+a_5(132)$} where $a_i \in \mathbb{Z}$.
But I have no idea how to get the coefficient of $e$ from here. Am I supposed to look for $a_0$?
How do I approach this problem?

$(e+(12))^2=(e+(12))(e+(12))=e\cdot e+e\cdot (12)+ (12)\cdot e+(12)^2=2e+2(12)$
