$7.($a$)$ Given a permutation, how does the number of inversions change when you swap any two adjacent elements of the permutation?

$($b$)$ Given two permutations A and B$.$ In each operation, you must swap any two adjacent elements in A and then swap any two adjacent elements in B$.$ What conditions do A and B must satisfy so that you can make the arrays identical using an arbitrary number of operations?

Hint $1$: If you swap two adjacent elements twice, the permutation doesn$$t change

Hint $2$: Try to make both permutations sorted