 So let's see how we multiply two matrices. So for example, we might multiply a two by two matrix by another two by two matrix. And so for example, I might take the matrix 3527 and multiply it by 1, negative 3, negative 2, 4. And so the important thing to remember about matrix multiplication is I'm going to take the rows of the first matrix and multiply by the columns of the second matrix. So my first product, the row 35, to be multiplied by the column, 1, negative 2. And I'm going to multiply and add them together. And I'm going to get negative 7, which is going to be my first row, first column entry. And I can find the other entries in the same way. So I'm going to take the first row, multiply by the second column, and multiply and add these terms. First row, second column, 3 times negative 3, 5 times 4. That gets me 11, which is my first row, second column entry in the product. And continuing in this fashion, second row times first column gives me my second row, first column entry, negative 12. And finally, second row, second column gives me my last entry, 22. And the matrices don't have to be the same size. So here I have a 2 by 3 matrix multiplied by a 3 by 1 matrix, sometimes called a column vector. And so that product, then I'll go first row times first and only column, gives me my first row, first column entry, second row, first column. That product will give me my second row, first column entry. And there's my product.