The question is for me to find the center of a group comprising of non singular square matrices of order n.

So if any member of the center is A, and G is any matrix in the group, we need AG = GA --> A = G-1 * A * G. (Where G-1 = G inverse)

I can intuitively say that only elements of the form A = nI satisfy this equation, but how do I prove it?

Please help