Proof that the identity element of a group is unique

A short video in which we prove that the identity element of a group is unique.

[ds]

Your explanations are so easy to understand and simple, and straight to the point💯, no unnecessary writing or talking, I am preparing for my exam and u are a huge help and u saved me from wasting my time to search other vids. U got a new sub, thank you.

[angelmendez-rivera]

In fact, with this proof, you can prove a much stronger statement. If (M, •) is a magma with left-identity L and right-identity R, then L = L•R = R, and so L = R = e is the unique two-sided identity element in M, and (M, •) is called a unital magma.

[mahidhar]

Please tell better to understand.i cant understood

[samanthajones]

Thanks for this video, it is a simple proof when you know how. The text book I had was very thin on the ground in terms of talking through the proof to see the steps all come together, your video was very helpful 😉

[VinayKumar-nfsd]

Can we use cancellation theorm to proove identity element uniqueness.. like a * e1= a*e2 and cancel out a?

[rahulchoudhary]

No this is wrong. The identity element must always come to the right of * operator. Thus your equation 2 is wrong.