Math, kinda

There is a type of math in the Exact Sciences called Alternate Units (coined by Grassmann). This incredibly confusing non-scalar mode of math using vectors of directed steps across a plane uses equations like 2 x 2 = 0, a^2 = 0, AB = -BA, and 2 x 3 = -3 x 2.
Why I'm writing this in an entry I have no idea. Anyway, it's confusing and I hope I wrote that right as it's just what I think the book 'Common Sense of the Exact Sciences' is trying to tell me about....