Science:Math Exam Resources/Courses/MATH152/April 2022/Question A20/Hint 1

Looking at how ${\textstyle A^{4}}$ acts on the eigenvectors, you should be seeing something that looks like ${\textstyle A^{4}{\vec {v}}_{1}=c{\vec {v}}_{1}}$, ${\textstyle A^{4}{\vec {v}}_{2}=c{\vec {v}}_{2}}$, ${\textstyle c\in \mathbb {C} }$. Using this, and the fact that linearly independent eigenvectors span ${\textstyle \mathbb {R} ^{2}}$, what can you conclude about ${\textstyle A^{4}}$?