order of permutations?

Question

In S_3 find elements a and b such that lal = 2 and lbl=2, but labl=3?

S_3 = {1,2,3}.
lal = the order of arbitrary permutation a in S_3.

Answer 1

Take a =
(1 2 3)
(1 3 2)
and b =
(1 2 3)
(3 2 1).
You can do the verification.

Answer 2

I'm confused. S_3 is the group of symmetric permutations on three things 1,2,3. Right?
What is |a|? An ablsolute value? Or is it l the lower case L? In which case, what is it? An arbitrary element?
I'd like a chance to do the problem. Please write:
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