# Order of Permutation Group

• Last Updated : 15 Mar, 2021

Order of Permutation-: For a given permutation P if  Pn= I (identity permutation) , then n is the order of permutation.

Let a permutation

and  Pn = I =

Then n is the order of permutation.

Example 1-:  How many times be multiplied to itself to produce

Solution-: Let      P=

Then P2=P.P=

P2=

P3= P2.P=

P3==I

Hence the required number is 3.

Order=3

Example 2-: Find the order of permutation .

Solution-:  Let the given permutation be P=

We can write P as P=

P2=

=

P3=P2.P=

=

P4=P3.P=

=

P4=I (identity permutation)

Hence, order is 4.

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