Suppose T and U are linear transformations from R n to R n such that T (Ux) x for all x in R n Is it true that U(Tx) x for all x in R n Why or why not

Question: Suppose T and U are linear transformations from R n to R n such that T (Ux) = x for all x in R n

Suppose T and U are linear transformations from Rⁿ to Rⁿ such that T (Ux) = x for all x in Rⁿ. Is it true that U(Tx) = x for all x in Rⁿ? Why or why not?

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