1. The problem statement, all variables and given/known data Prove the following theorem. If a≠0, then (a-1)-1=a Theorems proven before/axioms I am allowed to use: Existence of reciprocals axiom: there exist real numbers x and y where x≠0 such that xy=1 Possibility of division Thm: basically a-1=1/a 2. Relevant equations I just need a check on my proof since I am self studying the book. Any logical mistakes on my proof or suggestions etc? This is my first time writing proofs. 3. The attempt at a solution Assume (a-1)-1=a is true. Then by the existence of reciprocals axiom there exists an x such that (a-1)-1x=1. Hence, (a-1)-1x=axax=1Now by the possibility of division theorem we have, x=1/a=a-1Finally since we assumed (a-1)-1=a was true it follows that: (a-1)-1x=ax=aa-1=1Q.E.D It looks fine to me, I'm just a noob at proofs. Thanks.