Answer
True.
Work Step by Step
Let $\mathrm{A}$ be the standard matrix of $\mathrm{T}$,
and $\mathrm{B}$ be the standard matrix of $\mathrm{U}$.
Then, the the standard matrix of $\mathrm{T}(\mathrm{U}(\mathrm{x}))$ is $\mathrm{A}\mathrm{B}.$
Given that $\mathrm{T}(\mathrm{U}(\mathrm{x}))=\mathrm{x}$, it follows that $\mathrm{A}\mathrm{B}=\mathrm{I}.$
Both A and B are square n$\times$n matrices, so, by the IMT,
they are both invertible and $\mathrm{B}=\mathrm{A}^{-1}.$
By definition of inverse matrices, it follows that $ \mathrm{B}\mathrm{A}=\mathrm{I}$.
$\mathrm{B}\mathrm{A}$ is the standard matrix of $\mathrm{U}(\mathrm{T}(\mathrm{x}))$ so $\mathrm{U}(\mathrm{T}(\mathrm{x}))=\mathrm{x}$.
