Linear transforamtion

Question

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

Answer 1

Hi Tawa can you clarify the problem statement? What is T.Ux / Dx ? what does the "." mean and the "/" mean? It seems like it is asking whether matrix multiplication is commutative (AB =? BA). It is not.