Find the value

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,

$|A|+|B|=1-1=0$

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