Magic squares on Abelian groups

Let $(\mathrm{\Gamma },+)$ be an Abelian group of order $n^2$ and MS${}_{\mathrm{\Gamma }}(n)$ be an $n\times n$ array whose entries are all elements of $\mathrm{\Gamma }$. Then MS${}_{\mathrm{\Gamma }}(n)$ is a $\mathrm{\Gamma }$-magic square if all row, column, main and backward main diagonal sums are equal to the same element $\mu \in \mathrm{\Gamma }$. We prove that for every Abelian group $\mathrm{\Gamma }$ of order $n^2$, $n>2$, there exists a magic square MS${}_{\mathrm{\Gamma }}(n)$ where the square entries are elements of $\mathrm{\Gamma }$.