CHAPTER 03.14: BINARY OPERATIONS: Rules of binary matrix operations Part 4 of 4     In this segment we will talk about some of the rules for binary matrix operations and one we’ll talk about is the distributive law of binary operations. So if A and B are of size m by n, let’s suppose, so we have  a rectangular matrix of m rows and n columns both A and B and C and D are of size n by p. So n rows and p columns. Then the distributive law says two things – that hey, I can take the matrix A nd then I can multiply it to the addition of C and D.   So first I do the addition of C and D, then I multiply the resulting matrix to A. That will be the same as taking A multiply by C; taking A and multiplying by D. Again, we have to understand about sizes here. The number of columns of A has to be the same number of rows of C. The number of columns of A has to be the same as the number of rows of D, which is the case right here. And then the other one says that – hey – if I do the addition first, and then I multiply by another matrix – let’s suppose C – then that is the same as taking A multiplying that to C plus B times C.   The other side of the con is that – hey, let me take two matrices, add them together, then I’ll multiply by C. But that will be the same as multiplying A by C plus B times C here. Again, the order is important because the number of columns of A has to be the same as the number of rows of C. Number of columns B has the be the same as the number of rows of C, which is the case as per these assumptions, which we are making about A, B, C, and D. And that’s the distributive law for the binary operation of matrices. And that’s the end of this segment.