Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2017 / S19 / 1 / a / Solution

Take a reference point immediately before the focusing quadrupole and let matrices act on $(x,x^{\prime })$ from the right. With $q=1/f$, define $Q_F=\left(\begin{array}{cc}1& 0\\ -q& 1\end{array}\right)$, $Q_D=\left(\begin{array}{cc}1& 0\\ q& 1\end{array}\right)$ and $D(L)=\left(\begin{array}{cc}1& L\\ 0& 1\end{array}\right)$. One cell isIts determinant is one. A different starting point gives a conjugate matrix with the same trace and stability; the orthogonal transverse plane replaces $q$ by $-q$.