We know that for the elementary abelian group $G$ of order $p^n$, its automorphism group is $GL(n,\mathbb{Z}_p)$. Here we consider the group $G$ as a vector space over the field $\mathbb{F}_p\cong \mathbb{Z}_p$; and every automorphism is an invertible linear transformation of the vector space and conversely, so the automorphism group is $GL(V)\cong GL(n,\mathbb{Z}_p)$.
Is it true that the automorphism group of the abelian group $(\mathbb{Z}_{p^2})^n$ is $GL(n,p^2)$? (I think that it need not be true; I could not apply the technique of above group, because here the group $\mathbb{Z}_{p^2}$ is a ring, but not a field, so I can not consider the group as a vector space.)