Hint: A symmetric matrix over is diagonalizable, and the eigenvalues are real. What about the eigenvalues of ?
Let A be a symmetric matrix over the real numbers. A^10 = I. Prove A^2 = I.
I had this question in an exam but got 0/6 for it, so I'm not going to show my working here which was just wrong. How should I go about solving this question.