A problem about Abstract Algebra, please help!

[bananavsorange]

Let G be a finite groups, suppose φ : G → G given by φ(x) = x^3 is a homomorphism. The kernel of φ is Ker(φ) = {x ∈ G | x^3 = e}. Prove that |Ker(φ)| is an odd number. Which of the following proofs is correct?



I have no clues!

 

[Steven G]

Why do you have no clue? Can't you find any errors. Just go line by line in the proofs. Which lines are you unsure about whether they are true or not. Let us know and we can talk about them.