Question: 4. Suppose A is an nxn matrix with complex coefficients (i.e., coefficients in C). If A2 = -I, what are the possible eigenvalues of A?

4. Suppose A is an nxn matrix with complex coefficients (i.e., coefficients in C). If A2 = -I, what are the possible eigenvalues of A? If A has real coefficients (i.e., coefficients in R), show that n must be even. Give an example of a matrix A such that A2 = -I and A has real coefficients. Page 5

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