So given the following math question:
Given commutative ring $R$ and $n \in\mathbb{Z^+}$, show that the automorphism group $\text{Aut}(R^n)\cong \text{GL}_n(R)$ (the general linear group).
First, I found a counterexample with $R=\mathbb{Z}$ and $n=1$: the only automorphism of $\mathbb{Z}$ is the identity, yet $\text{GL}_1(\mathbb{Z})$ includes both $[1]$ and $[-1]$. Someone confirmed to me that the problem as stated is incorrect, and that the intended problem would feature modules instead of groups. Still, given my limited abstract algebra background, that does not enable me to reconstruct the problem as intended.
So, what is the problem supposed to say?
Thank you so much!