How to invert an 8x8 matrix or calculate 8DOF homography

Well I'm not sure what you actually want to do here. However to invert a 8x8 matrix (or any sized matrix) you can use my GaussMatrixF which is just an arbitrary sized matrix which can be solved by Gaussian elimination. It's meant to be setup as an augmented matrix and it will solve the first square part of the matrix into an identity matrix. So to solve an 8x8 matrix you would need to create a 8x16 matrix (8 rows, 16 columns) and place you original matrix in the left half. Fill the right half with the 8x8 identity matrix and call Solve. It's explained here.

Something like this:

 var gm = GaussMatrixF(16, 8);
 gm.rows[0].cols[0] = x1;
 gm.rows[0].cols[1] = y1;
 // [ ... ]
 // fill your whole 8x8 matrix
 // [ ... ]
 
 // initialize second half with identity matrix
 for(int r = 0; r < 8 r++)
 {
     for(int c = 0; c < 8 c++)
     {
         if (r == c)
             gm.rows[r].cols[8+c] = 1;
         else
             gm.rows[r].cols[8+c] = 0;
     }
 }
 
 if (gm.Solve())
 {
     // access inverted matrix by reading back columns index 8 to 15
 }