Solution
= Solution
A unit vector along the line is $v=(3,4)^T/5$. Reflection fixes its component parallel to $v$ and negates its perpendicular component, so the <reflection matrix> is
$$
\boxed{H=2vv^T-I=\frac1{25}\begin{pmatrix}-7&24\\24&7\end{pmatrix}.}
$$
Indeed $H(3,4)^T=(3,4)^T$, $H(-4,3)^T=-(-4,3)^T$ and $H^2=I$. These characterize the <orthogonal reflection> in that line.