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
multiply down and add...
and multiply up and subtract.