Question:
If $A=\left[\begin{array}{ll}0 & i \\ i & 1\end{array}\right]$ and $B=\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right]$, find the value of $|A|+|B|$.
Solution:
$A=\left[\begin{array}{ll}0 & i\end{array}\right.$
$\left.\begin{array}{ll}i & 1\end{array}\right]$
$\Rightarrow|A|=0-i^{2}$
$=-(-1)=1$
Also,
$B=\left[\begin{array}{ll}0 & 1\end{array}\right.$
$\left.\begin{array}{ll}1 & 0\end{array}\right]$
$\Rightarrow|B|=0-1=-1$
So,
$|A|+|B|=1-1=0$