>> Actually two kinds of multiplication. The first one is very predictable. It's called "scalar multiplication." Works like this, suppose we have a matrix A defined this way. For scalar multiplication we multiply times each item within the matrix. 2A means 2 times the entries here for the matrix and so we just double all of them. 2 times negative 2, negative 4. 2 times 1, 2. 2 times 3, 6. 2 times negative 1, negative 2. 2 times 0, 0. 2 times negative 4, negative 8. Highly predictable kind of thing. Now with this idea, we can actually write the expressions and simplify expressions in this matrix format. If this is matrix B then we can evaluate or simplify 2B minus 3A. Now we do it like this. 2B means 2 times matrix B, that's from up here, minus 3 times A. Well matrix A is the one from over here. And now we do the scalar multiplication business, double all of these entries and we get these. Now when we slide over here, we actually have two techniques that we can use. Minus 3, you see it's minus 3 times this. Now I have elected to take the technique where I'm gonna multiply 3 times all of these and then write minus, you see 3 times all of these. The other technique would be to say minus 3 times all of these and add the two matrices which ever way you'd like to do it is okay. But again, I'm doing this, I'm saying, "Okay, it's easier for me to multiply 3 times all these entries and then it's easy for me to subtract down here rather than add." So I'm thinking of it this way, 3 times negative 2, negative 6. 3 times 1, 3. 3 times 3, 9. 3 times negative 1, negative 3. I'm sure you get the picture. Now we have minus between these two and we subtract corresponding entries. So we would have 0 minus negative 6. That's 0 plus 6 or 6 for that entry. Then 4 minus 3 is 1. Then negative 8 minus 9, negative 8 with negative 9, that's negative 17. And then let's see, 6 minus negative 3, that's 6 plus 3, 9. Then 0 minus 0 is 0. And then negative 2 minus negative 12, that's negative 2 plus 12 or 10. Okay.