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) zero

Answer 1

Given, $\left|\begin{array}{cc}x& 2\\ 18& x\end{array}\right|=\left|\begin{array}{cc}6& 2\\ 18& 6\end{array}\right|$,
On expanding both determinants, we get
$x\times x-18\times 2=6\times 6-18\times 2\Rightarrow x^2-36=36-36\Rightarrow x^2-36=0\Rightarrow x^2=36\Rightarrow x=\pm 6$
So, (b) is the correct option.