multiplication between numbers is said to be commutative—when the order of the numbers does not influence the value of the product. this is true for the integers (whole numbers), e.g. 4 × 6 is the same as 6 × 4, and also for the rational numbers (fractions), and for all the other real numbers (representable as a field in the continuous line), and also for complex numbers (numbers representable as a field in the plane). however, it is not true for quaternions (numbers representable as a ring in the four-dimensional space), vectors or matrices.