I'm having trouble finding the identity of an operation. Could someone check my work?(adsbygoogle = window.adsbygoogle || []).push({});

I'm trying to find the identity of x*y = x + 2y - xy

In order to find the identity, I need to solve x*e = x for e

[tex]

\begin{align*}

x*e &= x\\

x + 2e - xe &= x\\

2e - xe &= 0\\

e(2-x) &= 0\\

\end{align*}

[/tex]

In order for e(2-x) = 0 to be true e = 0

Then I need to check if x*0 = x, which is true.

And then check if 0*x = x, which is NOT true, since 0*x = 2x.

So there is no identity and no inverse for the operation x*y = x + 2y - xy

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# Finding the Identity

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