Question:
If $\left|\begin{array}{cc}x & 2 \\ 18 & x\end{array}\right|=\left|\begin{array}{cc}6 & 2 \\ 18 & 6\end{array}\right|$, then $x$ is equal to
(A) 6 (B) $\pm 6$ (C) $-6$ (D) 0
Solution:
Answer: B
$\left|\begin{array}{cc}x & 2 \\ 18 & x\end{array}\right|=\left|\begin{array}{cc}6 & 2 \\ 18 & 6\end{array}\right|$
$\Rightarrow x^{2}-36=36-36$
$\Rightarrow x^{2}-36=0$
$\Rightarrow x^{2}=36$
$\Rightarrow x=\pm 6$
Hence, the correct answer is B.