your derivation states that:

A-B = A u B'

this is incorrect, you can use a Venn Diagram or the logic definitions of set operations to convince your self of the correct equation:

A-B = A n B'

as a result your derivation is changed thusly...

(A-B) n (B-A)= (A n B') n (B n A')

= A n (B' n B) n A' [Set intersection is associative]

= A n A' n (B' n B) [Set intersection is commutative]

= (A n A') n (B' n B) [Set intersection is associative]

= {} n {} [Intersection of complements is empty]

= {}