When two digits of thbase 10 representation of an inteer are intercharged, the diference bewen the old number and the new number is divisible by 9. Why? What happens in other bases?

Question

10A + B - 10B -A= difference.

This reduces to
9A - 9B
9(A-b)= difference.

Of course it is divisible by 9, it has a nine in it. Now what happens in other bases. Try this logic on say base 8.