katzface

You can probably put Beyonce in there too!

I can't understand the difference between the definitions of Identity and Invertibility - can someone explain?

I.e.:

Identity For any element a in G there is an element e where e⋆a = a⋆e = a.

Invertibility For each element a in G there is an element b where a⋆b = b⋆a = e, where e is the identity.