Huygens eyepiece - Cardinal Points

Can someone explain to me how I can get the cardinal points for Huygens eyepiece using the matrix method? I tried to solve it by considering two thin lenses and calculating the matrix for the system,

$$begin{bmatrix} 1&0 -1/f1&1end{bmatrix} begin{bmatrix} 1&d 0&1end{bmatrix} begin{bmatrix} 1&0 -1/f2&1end{bmatrix}, $$
where $d$ is the distance between the eye lens and field lens and $f_1$, $f_2$ is the focal length.
It gives me $c=0$, which gives the principal point at $infty$