Switch, switch, switchLogic Level 3
Let \(A\) and \(B\) are 2-digit positive integers, where \(A>B\) and \(A+B=100\).
If we switch the digits in \(B\) (call it \(B'\)), \(B'\) will be the product of both digits of \(A\).
If we switch the digits in \(A\) (call it \(A'\)), the absolute difference between the new \(A'\) and \(B\) will equal to \(B' + 1 \).
Find \(A \times B\).