Answer:
Observe that the set [tex]B=\{(1,0), (0,1)\}[/tex] is a basis for [tex]\mathbb{R}^2[/tex], then the matrix is defined by the image of the elements of B.
Since [tex]T(1,0)=(0,0)[/tex] and [tex]T(0,1)=(0,0)[/tex] then the associated matrix to T is [tex]A=\left[\begin{array}{cc}T(1,0)^T & T(0,1)^T\end{array}\right]=\left[\begin{array}{cc}0&0\\0&0\end{array}\right][/tex] that is the zero matrix.
