Science:Math Exam Resources/Courses/MATH221/December 2019/Question 04 (a)/Statement

In each of the following, indicate the correct answer (and only the correct answer) by circling the appropriate letter. You do not have to show your work in this question.

Let $M$ be the $2\times 2$ matrix such that ${\bf {x}}\mapsto M{\bf {x}}$ is the rotation by $90^{\circ }$ counterclockwise around the origin. What are the eigenvalues of $M$?

A: $\;0,\;i\quad$ B: $\;i$ (a repeated eigenvalue)$\quad$ C: $\;i,\;-i\quad$ D: $\;1+i,\;1-i\quad$ E: $\;{\frac {i\pi }{2}},\;-{\frac {i\pi }{2}}$