List of top Linear Algebra Questions on Simultaneous Triangularization and Commutators asked in GATE MA

Let \(P\) and \(Q\) be \(3 \times 3\) nonzero real matrices. Assume that there exists a \(3 \times 3\) real nonsingular matrix \(S\) such that \(S^{-1}PS\) and \(S^{-1}QS\) are both upper triangular. Which of the following statements is/are TRUE?