Hello,

the task is to prove that center of a matrix ring is the scalar matrices .

I found two more general proofs:

Center of an Algebra « Abstract Nonsense

The center of a matrix ring over a commutative ring is precisely the scalar matrices « Project Crazy Project

However I didn't understand those totally, so I coudn't reduce them to this simpler case. But I think the main point is:

Let's assume that and .

Matrix multiplication is commutative ( ) iff is in form .

I don't know how to continue etc., so any help is appreciated. Thanks!