Mistakes give rise to Problems- 4

Algebra Level 5

If you distribute the $\textbf{modulus}$ sign over the content in it, it's a mistake, i.e. $\left| a+b \right| = \left| a \right| + \left| b \right|$ This is a $\color{#D61F06}{\textbf{big mistake}}$ , it's a $\color{#3D99F6}{\textbf{false property}}$ !

But for how many pairs of integers $(a,b)$ such that $-10 \leq a \leq 10$ and $-10 \leq b \leq 10$ , is the above said "false" property seen to be "true" ?

Note:- $\left| a \right|$ means the absolute value of $a$ .