the inverse for any n by n matrix is as follows:

given matrix A, the inverse, A^(-1) is
(1/detA)*(Cij)^T 
where i and j are subscripts denoting matrix row and column,
det stands for determinate,
T stands for transpose,
Cij=(-1)^(i+j)*Mij,
Mij is the determinate of the (n-1) by (n-1) matrix formed by deleting
the ith row and jth column from A.

so in other words, given a 4 by 4 matrix:
   ( a11 a12 a13 a14 )
  (  a21 a22 a23 a24  )
A=(  a31 a32 a33 a34  )
   ( a41 a42 a43 a44 )

A^(-1)=(1/detA)* ( C11 C21 C31 C41 )
                (  C12 C22 C32 C42  )
                (  C13 C23 C33 C43  )
                 ( C14 C24 C34 C44 ) where C11,31,22,42,13,33,24,and 44
are positive and the rest are negative.

example of C11 (cross out row 1 and column 1):
        
       (a22 a23 a24)
C11=det(a32 a33 a34)
       (a42 a43 a44)
repeat this step for all C.

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