CHAPTER 03.13: BINARY OPERATIONS: Rules of binary matrix operations Part 3 of 4     In this segment we’ll talk about some rules of binary matrix operations. So let’s talk about the associative law of multiplication. And what is the association law of multiplication? That let there be an A matrix and let’s suppose this is M rows and n columns. Then B is n rows and p columns and C then has p rows and let’s suppose R columns. So we have three matrices, M rows and N columns, N rows and P columns and P rows and R columns. So the number of columns here are the same as the number of rows here, and the number of columns here is the same as the number of rows here. So be three matrices. Then in that case what’s going to happen is that if I take A times B times C here like this, what b times C has done first then its multiplied to A, will be same as multiplying A by B then multiplying by C.   So if we look at the association law of multiplication and say that hey let me go and do the B times C first, and then ill multiply it to A. And you’ll find out that it will turn out to be the same matrix as if you were going to multiply B by A and then multiply it by C. And these orders are extremely important because you can very well see that if this is M by N and this is N by P and this is P by R, only then we’ll find out that hey these matrix multiplications are valid. Same thing here - this M by N here, N by P here, and P by R here, only then those matrix multiplications are valid. And then the resulting matrix will be M rows and R columns. So if we call this to be, let’s suppose D, to be A times B times C, then because this is M rows and N columns, this is N rows and P columns and this is P rows and R columns. This resulting matrix D will have this many rows and this many columns. And that is the associative law of multiplication. And that is the end of this segment.