How to find the order of the elements of $A_4$? Just wondering how to find the order of each element in this group:
$A_4 = \{e,(123),(132),(124),(142),(134),(143),(234),(243),(12)(34),(13)(24),(14)(23)\}$
I tried writing each elements not in disjoint cycle but it didn't look right to me. I got 3 for all the cycles with 3, and 4 for the last cycles

Notice for any 3-cycle $(abc)$, $(abc)^2=(abc)(abc)=(acb)$, and $(abc)^3=(abc)^2(abc)=(acb)(abc)=e$, the identity.  Thus the order of any 3-cycle is 3.  
Noting that disjoint cycles commute, it is easy to see that $((ab)(cd))^2=(ab)(ab)(cd)(cd)=e*e=e$, so the order of any product of two disjoint transpositions is 2.
