How do you solve a 3 by 3 matrices that deals with cofactors?

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Go to this site and see exactly how one forms the inverse of
a 3x3 matrix using the minor-cofactor-adjoint method:

http://www.easycalculation.com/matrix/inverse-matrix-tutorial.php

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My problem:
 

This is a 4x4, not a 3x3.  It would be very long and difficult to find
the inverse of this 4x4 matrix by the the minor-cofactor-adjoint method.
But here is the inverse of the 4x4 matrix above:

  

Edwin