(Solved): Let \( T: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2} \) be the linear transformation that first rot ...

Let \( T: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2} \) be the linear transformation that first rotates points clockwise through \( 120^{\circ}(2 \pi / 3 \) radians \( ) \) and then reflects points through the line \( y=x \). Find the standard matrix \( A \) for \( T \). \[ A=[ \]