The operation \(*\) is defined by \(x * y = x + y - a\), where \(x\) and \(y\) are real numbers and \(a\) is a real constant.
(a) Prove that the set of real numbers, together with the operation \(*\), forms a group.
(b) State, with a reason, whether the group is commutative.
(c) Prove that there are no elements of order 2.
The operation \(\circ\) is defined by \(x \circ y = x + y - 5\), where \(x\) and \(y\) are positive real numbers. By giving a numerical example in each case, show that two of the basic group properties are not necessarily satisfied.