# Answer to Question #16539 in Algebra for Tsit Lam

Question #16539

Let p be a fixed prime. Show that any ring (with identity) of order p^2 is commutative

Expert's answer

If the additive order of 1 is

*p*2, then*R*= Z*·*1 is clearly commutative. If the additive order of 1 is*p*, then*R*= Z*·*1*⊕*Z*· a*for any*a**∈*Z*·*1, and again*R*is commutative.
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