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