The inverse of an odd permutati on isa)odd permutationb)even permutationc)even or odd permutationd)None ofthe aboveCorrect answer is option 'A'. Can you explain this answer?

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The inverse of an odd permutati on is

a)
odd permutation
b)
even permutation
c)
even or odd permutation
d)
None of the above

Correct answer is option 'A'. Can you explain this answer?

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Verified Answer

The inverse of an odd permutati on isa)odd permutationb)even permutati...

The question asks about the inverse of an odd permutation.

Key Points:

Parity of a Permutation:
- A permutation is called odd if it can be expressed as the product of an odd number of transpositions (two-element swaps).
- A permutation is even if it is expressed as the product of an even number of transpositions.
Properties of the Inverse:
- The inverse of a permutation has the same parity as the original permutation.
- This is because reversing the sequence of transpositions (to form the inverse) does not change the total count of transpositions, which determines the parity.
Application:
- If a permutation is odd, its inverse must also be odd because the parity remains unchanged.

Conclusion:

The inverse of an odd permutation is always an odd permutation.

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