Show that a reflection of each vector $\vec{x}=(x_1, x_2, x_3)$ through $x_3=0$ onto $T(\vec{x})=(x_1, x_2, -x_3)$ is linear.
I think it somehow involves the Transformation Matrix: $A=\begin{bmatrix}1&0&0 \\ 0&1&0 \\ 0&0&-1\end{bmatrix} \times \vec{x}$, resulting in $(x_1, x_2, -x_3)$ but i'm not sure. I'm wondering if it has something to do with the superposition principle but i'm also not sure.