Answer
$CZ=\left[ \begin{matrix}
-x \\
y \\
\end{matrix} \right]$ and it is a reflection about the $y\text{-axis}$ because the multiplication changes the sign of the $x\text{-coordinate}$.
Work Step by Step
To find CZ, multiply both matrices.
That is,
$$ $\begin{align}
& CZ=\left[ \begin{matrix}
-1 & 0 \\
0 & 1 \\
\end{matrix} \right]\left[ \begin{matrix}
x \\
y \\
\end{matrix} \right] \\
& =\left[ \begin{matrix}
-1\times x+0\times y \\
0\times x+1\times y \\
\end{matrix} \right] \\
& =\left[ \begin{matrix}
-x \\
y \\
\end{matrix} \right]
\end{align}$ $$
The multiplication changes the sign of the $x\text{-coordinate}$. Therefore, it is a reflection about the $y\text{-axis}$.
