assume A is a 2x2 matrix with real entries and A^4 = I and det(A) = -1, show that A^2 = I and Tr(A) = 0. so i was thinking of using eigenvalues and eigenvectors for this problem but i'm not sure because it's not guaranteed that the eigenvalues will be real. if they are real then i can just find an upper triangular matrix and show A^2 = I. do the assumptions imply that the eigenvalues will be real?