A half-wave plate causes the fast axis polarization component to lead the slow axis component by $\pi$ radians. The Jones matrix for this optic, oriented so that the fast axis is aligned with the y-axis, is
$\begin{equation*} M = \begin{pmatrix} 1 & 0\\ 0 & -1 \end{pmatrix}. \end{equation*}$
Explain why this is the correct Jones matrix.