Answer
See below
Work Step by Step
Given $T_1:V \rightarrow V\\
T_2:V \rightarrow V$
are linear transformations.
Obtain: $T_2T_1(v)=T_1^{-1}T_1(v)=v$
Let $T_2T_1(v)=w$
then $T_1[T_2T_1(v)]=T_1(w)$
Since $T_1(v)=T_1(w) \rightarrow v-w \in Ker (T_1)$
Suppose $Ker(T_1)=0 \rightarrow v-w=0 \rightarrow v=w$
Hence, $T_1(v)[T_1T_2]=T_1(w)\\
(T_2T_1)(v)=v$
for all $v \in V$
