Final answer:
The student's question pertains to whether the composition of two linear transformations is commutative. While t(ux) = x indicates that u is a right inverse of t, it doesn't ensure u(tx) = x without further information on the properties of t and u.
Step-by-step explanation:
The question involves linear transformations in mathematics. It states that if t and u are two such transformations with the property that t(ux) = x for all x, the student asks whether u(tx) = x also holds for all x. The given equations and quotes do not directly provide the answer to this question, but we can address whether the composition of two linear transformations is necessarily commutative.
In general, for two transformations t and u, t(ux) = x means that u is a right inverse of t. However, without additional information about t and u, we cannot assume that u is also a left inverse of t. This means we cannot conclude that u(tx) = x merely from the first equation; the transformations might not be commutative. The conditions under which they may be would require further exploration into the specific properties of t and u.