Answer
$A=\begin{bmatrix}
\cos(\frac{3\pi}{2}) & -\sin(\frac{3\pi}{2})\\
\sin(\frac{3\pi}{2}) & \cos(\frac{3\pi}{2})
\end{bmatrix}$
Work Step by Step
$A=\begin{bmatrix}
T(e_1) & ... & T(e_n)\\
\end{bmatrix}$
$e_1=\begin{bmatrix}
1\\
0
\end{bmatrix}$ and $e_2=\begin{bmatrix}
0\\
1
\end{bmatrix}$
$T(e_1)=\begin{bmatrix}
\cos(\frac{3\pi}{2})\\
\sin(\frac{3\pi}{2})
\end{bmatrix}$ and $T(e_2)=\begin{bmatrix}
-\sin(\frac{3\pi}{2})\\
\cos(\frac{3\pi}{2})
\end{bmatrix}$
$A=\begin{bmatrix}
\cos(\frac{3\pi}{2}) & -\sin(\frac{3\pi}{2})\\
\sin(\frac{3\pi}{2}) & \cos(\frac{3\pi}{2})
\end{bmatrix}$
