If $\left|\begin{array}{ll}2 & 4 \\ 5 & 1\end{array}\right|=\left|\begin{array}{cc}2 x & 4 \\ 6 & x\end{array}\right|$, then x is equal to :

$\pm \sqrt{3}$

$\left|\begin{array}{cc}
2 & 4 \\
5 & 1
\end{array}\right|=\left|\begin{array}{cc}
2 x & 4 \\
6 & x
\end{array}\right|$

$\Rightarrow (2)(1)-(4)(5)=(2 x)(x)-(6)(4)$

$\Rightarrow 2-20=2 x^2-24$

so $24+2-20=2 x^2$

$\Rightarrow 12+1-10=x^2$

$3=x^2$

$\Rightarrow x = \pm \sqrt{3}$