Thread: Identity Element

I would appreciate any help given on this problem in abstract algebra. I spent an hour trying to figure it out but with no luck

Let * be a binary operation on the nonempty set A. Prove that if A contains an identity element with respect to *, the identity element is unique. Prove using direct proof.

Originally Posted by TitaniumX

I would appreciate any help given on this problem in abstract algebra. I spent an hour trying to figure it out but with no luck

please don't put your question in quote tags.

i've never seen a direct proof for this.

let a and b be the identity elements. since a is the identity, a*b = b. but since b is the identity, a*b = a. thus, we have a = b.