How do you multiply matrices together?

Not all matrices can be multiplied together, so the first thing to do is check it's even possible! To do this write the matrices next to each other (we'll call the first one A and the second B). If the number of columns of A equals the number of rows of B, then they can be multiplied. Also, by doing this it will tell you the dimension of the product (i.e. AB) which will have the same number of rows as A and the same number of columns as B. From here it's just a case of arithmetic. Think of the entries of your new matrix as coordinate points. To calculate (i,j) (the entry in the ith row and jth column) you multiply the ith row of A by the jth column of B using the dot product for vectors. Then repeat this for each entry of AB.