I am fairly new to using Mathematica and was wondering if it's possible to define something along the lines of: $a*b=-b*a$ a sort of antisymmetry or skew symmetry if you will. I would like to do this so that when I multiply by some number say: $a*b*3=-b*a*3$ where the order in which the "a" and "b" are multiplied is preserved since there would be a antisymmetry. Hence, $\left(a*b*3 \right) + \left(b*a*3 \right)=0$ Would this be possible to do in Mathematica. Essentially what I would like to define is the following