CHAPTER 03.11: BINARY OPERATIONS: Rules of binary matrix operations Part 1 of 4     In this segment well talk about some of the rules of binary matrix operations. So let’s look at one of them called the commutative law of addition. What does that mean? That if A and B are m by n matrices - so what that means is that they are of size by m by n – so if you have A matrix which is of size M by n and B is of size m by n, then of course the addition is defined. What is the commutative law for addition? Is that hey if I add B to A, the same as adding A to B. That’s the commutative law of addition. Which makes sense because again this is a m by n matrix, a n by n matrix, the addition of course would be m by n matrix which would be the same as here. Then also that if I want to calculate the initial elements of A plus B, I’ll be taking the IJth element of A, and the B IJth element of B. Here if I was going to calculate this, it would b IJ element of B, and the A IJ element of A. And you can very well see that they’ll be the same number, whether I add this number to this number or whether I add this number to this number. And that’s what the commutative law of addition is telling us to do. And that’s the end of this segment.