Question:
If $\left[\begin{array}{ll}x & 1\end{array}\right]\left[\begin{array}{cc}1 & 0 \\ -2 & 0\end{array}\right]=O$, find $x .$
Solution:
$\left[\begin{array}{ll}x & 1\end{array}\right]\left[\begin{array}{cc}1 & 0 \\ -2 & 0\end{array}\right]=O$
$\Rightarrow\left[\begin{array}{ll}x-2 & 0+0\end{array}\right]=\left[\begin{array}{ll}0 & 0\end{array}\right]$
$\Rightarrow\left[\begin{array}{ll}x-2 & 0\end{array}\right]=\left[\begin{array}{ll}0 & 0\end{array}\right]$
$\Rightarrow x-2=0$
$\Rightarrow x=2$
$\therefore x=2$