For a 3x3 matrix you can use the mathmatical formaula directly.
|A|=a1*(b2*c3-b3*c2)-a2*(b1*c3-b3*c1)+a3*(b1*c2-b2*c1)
where the matrix is:
a1 a2 a3
A= b1 b2 b3
c1 c2 c3
I will try to work out the formula for larger matrices(it probably involves recursion). Try searching the net in the meantime.
Good Luck.