I'm in the process of doing some practice problems to better understand binary operations. I'm currently working on the following binary operation
On the set, $\mathbb{Z}$, the binary operation $a * b = a + 2b$
I've found that the operation is not associative and commutative (I could be wrong) but now when determining if this operation has an identity element, is it enough that the operation is non commutative and non associative to say that it has no identity element?
I guess to further strengthen the claim, I would look for cases where the identity element fails?
All help is greatly appreciated!
Thanks for looking!