If $P$ and $Q$ are invertible matrices $PQ=-QP$, then which claim about their traces is true? If $P$, $Q$ are invertible and $PQ=-QP$, then what can we say about traces of $P$ and $Q$.
I faced this question in an exam but according to me this question is wrong as $Q=-P^{-1}QP$, which implies $\det(Q)=0$ and it implies $Q$ is not invertible? But it is given invertible in hypothesis.
Options were both traces $0$, both $1$, $Tr(Q)\neq Tr(P)$ or $Tr(Q)=-Tr(P)$

Pre-multiply by $P^{-1}$ to  get $Q=P^{-1}(-Q)P$ which implies that matrices $Q$ and $-Q$ are similar, so $tr(Q)=tr(-Q)\implies tr(Q)=0$. Similarly you can get $tr(P)=0$ also.
