Prove or disprove - If a divides b and b divides a does a=b
Since $a,b \in \mathbb{Z^+}$, $a=b$ most definitely, as you have proved. You don't have to worry about negatives here if it is given that $a,b$ are positive integers. If $a,b \in \mathbb{Z}$, then a counterexample would be $a=−6,b=6$. Hence, unless $a,b$ are strictly positive, the statement is not true.