Find the matrix $A$ of the linear transformation $T$ from ${\mathbb R}^2$ to ${\mathbb R}^2$ that rotates any vector through an angle of $120 ^\circ$ in the counterclockwise direction.

$A=$ $\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$