Question:
If $x \in \mathrm{N}$ and $\left|\begin{array}{cc}x+3 & -2 \\ -3 x & 2 x\end{array}\right|=8$, then find the value of $x$.
Solution:
$\left|\begin{array}{cc}x+3 & -2 \\ -3 x & 2 x\end{array}\right|=8$
$\Rightarrow(x+3) 2 x-(-2)(-3 x)=8$
$\Rightarrow 2 x^{2}+6 x-6 x=8$
$\Rightarrow 2 x^{2}=8$
$\Rightarrow x^{2}-4=0$
$\Rightarrow x^{2}=4$
$\Rightarrow x=2 \quad[x \neq-2 \because x \in \mathrm{N}]$