To find the inverse of a permutation given in cycle notation, we simply reverse the order of elements within each cycle.

Given the permutation $(2 3 4 5)(1 7 6)$, we proceed as follows:

1. Inverse of the first cycle $(2 3 4 5)$:
   Reverse the order of the elements in the cycle: $(2 3 4 5)^{-1} = (5 4 3 2)$

2. Inverse of the second cycle $(1 7 6)$:
   Reverse the order of the elements in this cycle: $(1 7 6)^{-1} = (6 7 1)$

So, the inverse of the permutation $(2 3 4 5)(1 7 6)$ is: $(5 4 3 2)(6 7 1)$

Summary of steps:

• Reverse the order within each cycle.
• The inverse of $(2 3 4 5)(1 7 6)$ is $(5 4 3 2)(6 7 1)$.

Would you like more details on how this process works or any further clarification?

Here are 5 related questions you may find interesting:

1. How do you find the inverse of a permutation in two-line notation?
2. What happens if a cycle is of length 1? How does this affect the inverse?
3. Can you find the inverse of a product of two cycles?
4. How do you perform the composition of two permutations?
5. What is the inverse of a transposition (a 2-cycle)?

Tip: Always reverse the order of elements in each cycle when computing the inverse.