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## Homework Statement

Given a set R={x,y,a,b}

There are 2 tables shown: one is the addition of x,y,a,b elements with x,y,a,b elements. The 2nd table is multiplication of each element with the other elements. (The 2nd table shows that x multiplied by anything equals x)

we have a+b=y and (a)(b)=y

Decide which elements must be the 0 and the 1, then prove that this is a commutative ring with unit.

## The Attempt at a Solution

I know how to show it is commutative. I'm just having trouble starting on it.

Well if the addition of a and b equals the multiplication of a and b, then a=b=y=0. Is this right? But then since x multiplied by anything equals x, then x must also be 0. But then there is no element 1. So how can I show commutativity with this??

Also don't know how to show that there exists units.

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