 So something else we're going to want to do is to be able to find the inverses mod n of a matrix. So let's take a look at this problem. So here I have a 2 by 2 matrix 3, 2, 4, 7, and I want to find the inverse, but what we'll do that's a little bit different here is we'll try and find this inverse now mod 36. So our process is actually fairly close to what we do for finding the inverses of a matrix under normal circumstances. We'll use the co-factor method. So first we'll find the matrix of co-factors. So we'll go ahead and put down our checkerboard of pluses and minuses. And then remember that the next step in the co-factor method, we want to find the determinant of what's left over when we wipe out an entry's row and column. So for our first entry, we'll wipe out the row and column of that entry and what's left over just 7 and the determinant of a 1 by 1 matrix is just the number itself. And that's going to be assigned the value 7 plus 7. So likewise we'll go to the next row, we'll go to the next entry, wipe out that row and column and enter it in, and this time we have a minus associated with that value. And we'll keep doing this for the other entries in the matrix and we'll get our matrix of co-factors. Next we want to transpose the matrix of co-factors and then multiply by the reciprocal of the determinant. Now in real number arithmetic, the reciprocal of the determinant is easy to find. Because we're working mod 36, what we need to do is we need to find the reciprocal, the multiplicative inverse of the determinant mod 36. So we find our determinant first. So our original matrix 3, 2, 4, 7 has determinant 13 and we're in luck 13 does have a multiplicative inverse mod 36. We just have to find it. So we'll solve our diathontine linear equation 13 times what gives you some multiple of 36 plus 1. And we get a solution x equals 25, y equals, well we don't really care what y is, that doesn't really matter. So the inverse of 13, our determinant is 25 and so I'll take my matrix and multiply it by 25 to get the inverse of the original matrix. And remember we're working mod 36, so there really isn't any reason to carry around large numbers and I'll reduce those and I'll get the inverse of the matrix mod 36.