I am having trouble understanding this example:(adsbygoogle = window.adsbygoogle || []).push({});

Let G=S_3 and H={(1),(13)}. Then the left cosets of H in G are

(1)H=H

(12)H={(12), (12)(13)}={(12),(132)}=(132)H

I cannot figure out how to produce this relation:

(12)H={(12), (12)(13)}={(12),(132)}=(132)H

I understand (12)H={(12), (12)(13)} but not how (12)(13) = (132) or the equivalence after that...

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# Cosets of a subset of S_3

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