Let be positive integer and let .

a. Show that is a group.

b. Show that

For a ---

Associativity -

I defined binary operation as .

And therefore this is not associative and is not a group.

Just for practice, I continued to the other axioms of a group.

Identity element -

I said there was no identity element, because for any value of e, and would leave a remaining x term paired with an n.

When I try e=1, I get

Which are both not x.

When I try e=-x, I get

Which are both not x.

So how do I prove that there is no identity, and if there is, how do I find it? I'm not not able to spot it right off the bat, am I doomed? Is there any sort of loose procedure?

For the third axiom, the existence of an inverse, I said there was none because there is no identity element. I made this argument based on the equation in my book,

. Since e doesn't exist, I figured there can't be an inverse.

For b ---

I don't even know how tostartthis, so I'm just going to cross that bridge when I get to it.

I know this is all completely wrong, any help is appreciated.