Hello, i need help doing a proof, im pretty sure on how to do it but not that way my teacher wants it. He wants it in a chart form by taking splitting up both side.

Question

i have to show that |a-b|=|b-a|

Answer 1

If a>b, it becomes a-b = a-b
If a<b, it becomes b-a = b-a
If a=b it becomes 0 = 0
So it is always true