My textbook claims:
I don't understand how D can be true. Say I have a 2x4 matrix and I multiply it by the 4x2 zero matrix. I get a 2x2 zero matrix. Now assume I multiplied in the other order, I multiply the 4x2 zero matrix against the 2x4 matrix. I get the 4x4 zero matrix. They are both zero matrices, but they have different dimensions! Surely they can't be considered equal in this case?