Uniqueness of inverse element : Group Theory
Theorem : In a group G, inverse of any element is unique. Proof : Let G be a group with the identity element e. Let a 𝞊 G. Since G is a group, a has an inverse element say b. Now we prove b is only the inverse element of a in G. In contrary, assume c is also the inverse of a in G. To prove a has unique inverse element , we have to prove b = c. Since b is inverse of a in G, we have a b = e = b a ............I ...