The preimage $\preimage{T}{3}$ is the set of all matrices
$\begin{bmatrix} a & b\\c & d\end{bmatrix}$
so that
$\lt{T}{\begin{bmatrix}a & b \\ c & d \end{bmatrix}} = 3$.
A matrix
$\begin{bmatrix} a & b\\ c & d \end{bmatrix}$
is in the preimage if
$a + b + c - d = 3$,
i.e. $d = a + b + c - 3$.
This is the set. (But the set is not a vector space. Why not?)
\begin{align*}
\preimage{T}{3} &=
\setparts{\begin{bmatrix} a & b \\ c & a + b + c - 3\end{bmatrix}}{a,b,c\in\complexes}
\end{align*}