Question

prove that inverse of any element in a group is uniaue​

Answer 1

In a group (G,*) every element has a unique inverse.

Proof: if x€G and y1 and y2 are both inverse of x.

Then y1= y1×e (bcoz e is the identity)

= y1×(x×y2) bcoz y2 is the inverse of x.

= (y1×x)×y2 by associative law

= e×y2 bcoz y1 is the inverse of x.

= y2 bcoz e is the identity

So y1=y2 hence the proof.