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I'm having some trouble trying to solve this question.. Any advice/help is appreciated!

## Homework Statement

Suppose that a and b belong to a group such that:

|a| = 4, |b| = 2, and suppose a

^{3}b=ba

Find the order of ab.

## Homework Equations

## The Attempt at a Solution

So I am unsure of which theorems I should be looking at... but anyways...... my horrible attempt:

so a,b are in G.

|ab| = (ab)

^{n}= 1

Let n = order(ab), a

^{n}b

^{n}= 1 --> a

^{n}=b

^{-n}

I don't know if I should continue from this point because I don't know how exactly I would go about finding the order.

I think |ab| = |ba|, yes or no?

If it does then I'm guessing I can use that to find the order of a

^{3}b?

Any hints or suggestions on how?

Thank you.