# Show that a ring is commutative if it has the property that ab = ca implies b = c when a != 0.

Show that a ring is commutative if it has the property that ab = ca implies b = c when $a\ne 0$.
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Since R is ting, therefore by propery of ring we have,
a(ba)=(ab)a for all $a,b\in R$
Now, applying given condition on the above property, we get
ba=ab for all $a,b\in R$
Therefore, R is cpmmuttive ring
Hene, proved