Chapter 3.15, Problem 10MP

The following matrix product is used in discussing two thin lenses in air: $M=\left(\begin{array}{cc}1& -1/f_2\\ 0& 1\end{array}\right)\left(\begin{array}{cc}1& 0\\ d& 1\end{array}\right)\left(\begin{array}{cc}1& -1/f_1\\ 0& 1\end{array}\right),$ where $f_1$ and $f_2$ are the focal lengths of the lenses and d is the distance between them. As in Problem 9, element $M_{12}$ is $-1/f$ where f is the focal length of the combination. Find M, detM, and $1/f.$