[Math] the order of the alternating group $A_4$

Question

When I write out all the elements of $S_4$, I count only 11 transpositions. But in my text, the order of $A_4$ is $12$. What am I missing?

$A_4=\{(12)(34),(13)(24),(14)(23),(123),(124),(132),(134),(142),(143),(234),(243)$

$|A_4|=11$

Answer 1

You are missing the identity element. It can be written as an "even" permutation: $$(12)(12)$$