For some constants $a$ and $b,$ let The function $f$ has the property that $f(f(x)) = x$ for all $x.$ What is $a + b?$

$f(x) = \left\{ \begin{array}{cl} ax + b & \text{if } x < 2, \\ 8 - 3x & \text{if } x \ge 2. \end{array} \right.$