Let $ X_1, X_2, \ldots, X_5$ be fixed $ 6 \times 6$ matrices over $ \mathbb{Z}_5$ . I want to find(if exist) $ 6 \times 6$ matrices $ M_1, M_2, \ldots, M_6$ such that $ M_i \neq 0 $ , $ tr(X_i. M_k. X_j. M_k^{-1}) = 0$ and $ tr(X_i. M_l^{-1}.M_k. X_j. M_k^{-1}.M_l) = 0$Read more
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