Linear Algebra

Given two matrices of the same size whose columns all sum to 1, the (cross) product of those will also have columns that total to 1.

 A * A-1 = A-1 * A = I

but

 A * B ≠ B * A

Given

 A * B = C

where

 Size(A) = Ax, Ay
 Size(B) = Bx, By

then

 Ay == Bx (or error)
 Size(C) = Ax, By