If a and b are slopes of the angular bisectors of the coordinate axes then ${\mathrm{a}}^2+{\mathrm{b}}^2$ is 

The angular bisectors of coordinate axes are $\mathrm{x}+\mathrm{y}=0$ and  $\mathrm{x}-\mathrm{y}=0$
Slopes are  $\mathrm{a}=-1,\mathrm{b}=1$  
It implies that  
$\begin{array}{c}{\mathrm{a}}^2+{\mathrm{b}}^2=1^2+{\left(-1\right)}^2\\ =1+1\\ =2\end{array}$  
Therefore, ${\mathrm{a}}^2+{\mathrm{b}}^2=\boxed{2}$