Let (G,*) be an arbitrary group. Prove that any element of this group has exactly one...

 

Transcribed Image Text:

Let (G,*) be an arbitrary group. Prove that any element of this group has exactly one inverse. [Hint: assume x has two inverses y1, y2 and consider associativity for y1 *x * y2 ] Let (G,*) be an arbitrary group. Prove that any element of this group has exactly one inverse. [Hint: assume x has two inverses y1, y2 and consider associativity for y1 *x * y2 ]