Ques-1-Let-G-be-a-group-then-show-that-for-each-a-G-a-unique-element-e-G-a-e-e-a-a-Ques-2-If-a-G-x-G-and-x-is-unique-show-that-if-x-a-e-then-a-x-e-Hello-

Question Number 191986 by Mastermind last updated on 04/May/23

Ques . 1

Let (G, *) be a group, then show

that for each a \in G, \exists a unique

element e \in G ∣ a * e = e * a = a

Ques . 2

If a \in G \Rightarrow x \in G and x is unique

show that if x * a = e, then a * x = e .

Hello!

Answered by AST last updated on 04/May/23

Q u e s . 1 f o l l o w s f r o m t h e p r o p e r t y o f a g r o u p

t h a t f o r e v e r y a \in G, \exists a u n i q u e e l e m e n t

e \in G ∣ a * e = e * a = a

2) x * a = e \Rightarrow x^{- 1} * x * a = x^{- 1} * e \Rightarrow a = x^{- 1} * e

\Rightarrow a * x = x^{- 1} * e * x = x^{- 1} * x * e = e

Commented by Mastermind last updated on 04/May/23

Thank you so much sir