Determine the center of the group $GL_n(\mathbb{R})$.
The center of a group $G$ is the set of elements that commute with every element of $G$. I think the answer is $Z(GL_n(\mathbb{R}))=\{\lambda \times I $|$ \lambda \in \mathbb{R}\}$, where $I$ is the identity matrix. However I'm not sure how to prove it. Is this correct? And if so, what's a good way to go about showing this is the center of the group?
