Here's a question.
I understand how to prove that it's associative but I don't understand how it's proved to have an identity element.
Also, I understand that for identity, $(x,y,z) * (e,f,g) = (e,f,g) * (x,y,z) = (x,y,z)$
Here's how it's proved.
Where did the $(0,0,1)$ come from?
Also the $(1,1,1)$ used to prove that it's not invertible, where did the that come from?