Solution
= Solution
Among the two <orthogonal matrices> from part (d)(i), $d=-1$ gives $L=-I$, a <rotation matrix> through angle $\pi$. For $d=1$, the <determinant> is $-1$, so the matrix reverses orientation and is a reflection rather than a rotation:
$$
\boxed{b=c=0,\qquad d=1,\qquad L=\begin{pmatrix}-1&0\\0&1\end{pmatrix}.}
$$
It is the <reflection matrix> across the $y$ axis.