As in adding scalar quatities, changing the order in which to vectors are added does not affect the final resultant vector. In other words A + B = B + A. Thus I could take vector A and add it to B and the final resultant vector will not change. However, subtracting vectors is NOT Commutative. This is because vector A and B are not the same (most of the time) and a negative sign affects a vector's direction. Thus A - B != B - A.