It's about where "e", the identity element, is placed - in the "identity" rule it is one of the terms of the operation (e * a, a * e) while in the "invertibilit

It's about where "e", the identity element, is placed - in the "identity" rule it is one of the terms of the operation (e * a, a * e) while in the "invertibility" rule it's the result of the operation. If you want an example, think Z (integers) and "+": there is an element of Z, namely zero (0), where the identity rule tells us that x + 0 = 0 + x = x and the invertibility rule says that for any x in Z, there is an y in z such that x + y = 0