= Solution
Choose the $z$-axis along the line of intersection of the two planes. Their unit normals lie in the $xy$-plane; after choosing the $x$-axis, take
$$
n=(1,0,0),
\qquad
m=(\cos\theta,\sin\theta,0),
$$
where $\theta$ is the oriented angle between the planes. The two <reflection matrix>[reflection matrices] restrict to
$$
H_n=\begin{pmatrix}-1&0\\0&1\end{pmatrix},
\qquad
H_m=\begin{pmatrix}
-\cos2\theta&-\sin2\theta\\
-\sin2\theta&\cos2\theta
\end{pmatrix}
$$
on the $xy$-plane and both fix the $z$-axis. Their product is
$$
H_mH_n=
\begin{pmatrix}
\cos2\theta&-\sin2\theta\\
\sin2\theta&\cos2\theta
\end{pmatrix}.
$$
\b[Thus the <composition of two plane reflections> is a rotation about the intersection line through angle $2\theta$.]
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