Exercise
The inverse of the permutation (1,3,5,7)(2,4,6) in S7 is
(2,4,6)(1,3,5,7)
(7,5,3,1)(6,4,2)
(7,5,3,1)(2,4,6)
No, it is the element itself.
Yes.
No, why should the first cycle be inverted and not the other?
Exercise
The inverse of the permutation (1,3,5,7)(2,4,6) in S7 is
(2,4,6)(1,3,5,7)
(7,5,3,1)(6,4,2)
(7,5,3,1)(2,4,6)