Find (e) such that (a * e = a \Rightarrow a+e+ae = a \Rightarrow e(1+a) = 0). Since (a \neq -1), (e = 0). Check: (0 * a = 0 + a + 0 = a). So identity is (0).

This guide provides a roadmap to the solutions, explaining the "how" and "why" behind the problems in each major chapter.