Solution
= Solution
The coefficient $\langle e(t),\omega\rangle$ is nonzero exactly when every column of $t$ meets every row of $\omega$ in at most one entry. Permuting equal-length rows of $\omega$ preserves this condition, and the same holds with $u$ in place of $t$. Therefore membership in $A_{tu}$ is constant on each class of the stated <equivalence relation>, so $A_{tu}$ is a union of equivalence classes.