Abstract Math

Prove that (Z; #), where a#b = a + b + 1, is a group (i.e. prove that # is associative, that there is an identity element, and that every element has an inverse).

hint 1: For proving that the system has an identity element, we can provide an example such as e=0, and then show that it works as an identity element

hint 2: to solve if something is associative, we need to prove that (a∗b)∗c=a∗(b∗c). For this question, there is only one operation, #, so you would start with (a#b)#c

hint 3: a, b, and c are arbitrary integers here.