I'm wondering whether this question is wrong...
It says show that $\operatorname{orb}(p)$ where $p=[1,1]$ is the set $\{[x,y]: xy\neq0\}$ but if we apply the matrix $\begin{bmatrix}1&0\\1&-1\end{bmatrix}$
we get the vector $[1,0]$ which has $xy=0$.
Is it me or the book who is wrong or am I missing the point completely?