Given permutation are,
a=[1324354251] and b=[1523324451]
Now ,ab=[1324354251][1523324451]
=[1125344253] =(2 5 3 4 )
=(2 4)(2 3)(2 5)
Since ,Every permutation in Sn,n>1, is a product of 2-cycles.
However this is not the only way a permutation can written as a product of 2-cycles but the number of 2-cycles are always equal
i,e if α∈Sn and α=β1β2.......βr and α=γ1γ2.......γs
Where β′s and γ′s are 2-cycles.
Then r=s.
Again we known that , A permutation that can be expressed as a product of an odd number of 2-cycles is called an odd permutation.
Hence, ab is an odd permutation.
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