Let $T: {\mathbb R}^2\rightarrow {\mathbb R}^2$ be the linear transformation that first reflects points through the $x$-axis and then then reflects points through the line $y=-x$. Find the standard matrix $A$ for $T$.

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