This is a trick that ONLY works for 3 x 3's.  You cannot use it for  4 x 4's and higher...  For these, the formal approach is a gnarly thing that expands around a row or column and uses critters called "minors."  However, I highly recommend a computer or graphing calculator.  If you go on to take Calculus 3 or Linear Algebra, you'll need the "real" 3 x 3 technique, but it will be specialized and really easy to pick up.

On to the trick...

It works a lot like the 2 x 2 method where you