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
$T(x,y)=(x+y,3x+3y)$
Then, we have
$T(1,0)=(1,3)\\ T(0,1)=(1,3)$
Therefore, the matrix corresponding to the linear transformation $T$ is given by:
$A=[T(e_1)$ $T(e_2)]$ $=\left[ {\begin{array}{*{20}{c}} { 1}&1\\ 3&{ 3} \end{array}} \right]$
Since $A$ is not invertible, then $T$ is not invertible.
