Question: Let A E M2(R) be a rotation matrix not equal to I or I. Find the two complex eigenspaces U and V of A in

Let A E M2(R) be a rotation matrix not equal to I or I. Find the two complex eigenspaces U and V of A in the form U = Span(u) and V = Span(v), 1Where u and v are suitable complex eigenvectors. Hint: If A = (2:3)) _:HSE:D , whet are the complex eigenvalues in items of 9:? Note that, although the eigenvalues depend on 6, the eigenspaces do not. This fact is an instance of a broader phenomenon concerning matrices that commute. Please ask to learn more

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