Prove that the center of the ring $M_n(R)$ is the set of scalar matrices. I know what a center look like but i feel like i have not enough information to even solve this problem. Anyone that can help that would be great.


marked as duplicate by Michael Albanese, rschwieb ring-theory Feb 5 '15 at 20:31

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  • $\begingroup$ Double containment is the best way to do it. Let $Z$ be the center and $D$ be the set of scalar matrices. Certainly scalar matrices are contained in the center, as $A(\lambda I) = \lambda (A I) = \lambda A = (\lambda I)A$. The other direction is a little harder. Try direct computation of a non-scalar matrix. $\endgroup$ – walkar Feb 5 '15 at 20:31
  • $\begingroup$ Please search for your question before posting your question. $\endgroup$ – rschwieb Feb 5 '15 at 20:32

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