1. The problem statement, all variables and given/known data If a 3 x 3 matrix A is diagonalizable with eigenvalues -1, and +1, then it is an orthogonal matrix. 2. Relevant equations 3. The attempt at a solution I feel like this question is false, since the true statement is that if a matrix A is orthogonal, then it has a determinant of +1 or -1, which has nothing to do with diagonalozation. However, I don't see how to prove this rigorously. Would the best way just be to search for a counter-example?