The order of an element, |a| , is defined as thesmallest possibleinteger n such that . Immediately you should notice that this rules out infinity as a possiblity as we're given that , and clearly 6 < infinity .

Since we're given it must be that |a|divides6 . This gives the possibilites:

1) |a| = 1

2) |a| = 2

3) |a| = 3

4) |a| = 6

You can test to see if our original equation is satisfied:

Suppose |a|= 2, then is still true that ? Well, and we know that |a| = 2 and so

therefore . So it still is true. If you're not convinced you can repeat this for the other cases.

Hope this helps.

Pomp