Find the orthogonal vectors $v_1$ and $v_2$ such that $Av_1$ and $Av_2$ are still orthogonal, where $$A = \begin{pmatrix} 1 & -1 \\ 2 & 2 \end{pmatrix}$$
What can we comment about the lengths of $Av_1$ and $Av_2$ ?
I'm stuck thinking if these $v_1$ and $v_2$ are eigenvectors of $A$. If yes how does the second condition hold, "$Av_1$ and $Av_2$ are still orthogonal"? Is it by default? Thanks in advance!