Determinates

1      2   3       1    2
2      4   6        2   4
17  18  19      17  18

76+204+108-76-108-204=0

First of all, there are different types of maxtrices.  There can be a 2*2, 3*3, 4*4, and many more.  There is different ways to find the determinates of each also.  For a 2*2, all you have to do is multiply diagonally and then subtract them.  For a 3*3, which is what we have here, you do something completely different than you would with a 2*2 matrice.  For 3*3 matrices, you have to recopy the first two columns.  Once you do that, you have to multiply diagonals.  You have to add the diagonals that are going right and you subtract the diagonals that go left.  Once you do all of the stuff you just add and subtract all the numbers together and you have your answer.  For this problem we are given the answer I calculated was zero.  All the numbers canceled out, which makes it easier to solve!