Show the center of the general linear group are the proportional diagnol matrices.

Meaning, .

I try to explain this so it makes it more elementary. The set is the set of all invertible matrices having as their entries. This set is called the "general linear group". The "center" of this set are all the matrices which commute with everything else. So you need to show if a matrix commute with all invertible matrices then it must be a proportional diagnol matrix.