Answer
$T$ is not invertible.
Work Step by Step
Take the standard basis for $R^2,$ which is $\{(1,0),(0,1)\}=\{e_1,e_2\}$
We are given
$T(x,y)=(2x,0)$
Then, we have
$T(1,0)=(2,0)\\ T(0,1)=(0,0)$
Therefore, the matrix corresponding to the linear transformation $T$ is given by:
$A=[T(e_1)$ $T(e_2)]$ $=\left[ {\begin{array}{*{20}{c}} { 2}&0\\ 0&{ 0} \end{array}} \right]$
Since $A$ is not invertible, then $T$ is not invertible.
