Inverse of a Permutation:
A permutation is an arrangement of objects in a particular order. In mathematics, we often deal with permutations of a set of numbers. The inverse of a permutation is obtained by reversing the order of the elements in the permutation.

Even and Odd Permutations:
In permutation theory, we classify permutations as even or odd based on the number of inversions they have. An inversion in a permutation occurs when two elements are in reverse order. For example, in the permutation (2, 4, 1, 3), there are three inversions: (2, 1), (4, 1), and (4, 3).

Inverse of an Even Permutation:
When we take the inverse of an even permutation, the resulting permutation will also be even. This can be proven by considering the number of inversions in the original permutation and its inverse.

Proof:
Let's assume we have an even permutation P with n inversions. We also have its inverse, denoted as P^-1. Now, we need to show that P^-1 is also an even permutation.

When we take the inverse of P, the order of the elements is reversed. This means that each inversion in P becomes a non-inversion in P^-1, and each non-inversion in P becomes an inversion in P^-1.

Since an even permutation has an even number of inversions, reversing the order of the elements doesn't change the parity of the number of inversions. Therefore, P^-1 will also have an even number of inversions, making it an even permutation.

Conclusion:
Based on the above proof, we can conclude that the inverse of an even permutation is always an even permutation. Therefore, the correct answer to the given question is option 'B' - even permutation.