Let $A$ be a $2 \times 2$ orthogonal matrix such that $\operatorname{det}(A) = -1$. Show that $A$ represents reflection about a line in $\mathbb{R}^2$.
Let $A$ be a $2 \times 2$ orthogonal matrix such that $\operatorname{det}(A) = -1$. Show that $A$ represents reflection about a line in $\mathbb{R}^2$.