Hey guys, so I have the following question...

Suppose we have the operator $. Let s be a left identity for $ (s$x = x for all x) and let r be a right identity for $ (x$r = x for all x). Formally prove that s = r.

Here is my approach so far...

Code:

a $ s = a
a $ r = a
s $ r = s $ r = s
= s $ r = r
So, s = r

I don't think that this is right. And if it is right, it does not show why. Does anybody have any input as to whether or not what I have is good or how you would go about it? It's important that I show why I do what I do...

Thanks!