Answer
$A=\left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 1\end{array}\right]$
Work Step by Step
To get matrix of $T,$ we must find $T\left(e_{1}\right), T\left(e_{2}\right), T\left(e_{3}\right)$
Then, matrix is $\left[\begin{array}{lll}T\left(e_{1}\right) & T\left(e_{2}\right) & T\left(e_{3}\right)\end{array}\right]$
$T\left(e_{1}\right)=T(1,0,0)=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right]$
$T\left(e_{2}\right)=T(0,1,0)=\left[\begin{array}{c}0 \\ -1 \\ 0\end{array}\right]$
$T\left(e_{3}\right)=T(0,0,1)=\left[\begin{array}{l}0 \\ 0 \\ 1\end{array}\right]$
$A=\left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 1\end{array}\right]$
