Question

Find the order of each permutation.

(b) ( 123 )

Short answer

The order of a permutation ( 123 ) is 3.

Step-by-step solution

Step 1:Order of a permutation

Theorder of a permutation$\sigma$ is the smallest positive integer $n$such that${\sigma }^n=\in$ where $\in$is the identity permutation.

Order of a permutation ( 12 )

Apply the permutation $\sigma$twice then,

Now, apply the permutation $\sigma$thrice then,

Here, $n=3$is the smallest positive integer such that${\sigma }^3=\in$

Therefore, the order of a permutation ( 123 ) is 3.