ISRO2008-31

Question

If the two matrices $\begin{bmatrix} 1 &0 &x \\ 0 & x& 1\\ 0 & 1 & x \end{bmatrix}$ and $\begin{bmatrix} x &1 &0 \\ x & 0& 1\\ 0 & x & 1 \end{bmatrix}$ have the same determinant, then the value of $x$ is  

• A. $\frac{1}{2}$
• B. $\sqrt2$
• C. $\pm \frac{1}{2}$
• D. $\pm \frac{1}{\sqrt2}$

Answer 1

Determinant of $1^{st}$ Matrix $ = x^2 - 1$
Determinant of $2^{nd}$ Matrix $ = -x^2 -x$

Both are equal:
$x^2 - 1 = -x^2 - x$
$2x^2 + x -1 =0$

Solve.

$x = \frac{1}{2}$

Comments

@Sachin Mittal 1

x = -1, 1/2

but in the options only 1/2 is given that's why we are discarding x=-1. 

Otherwise both x=-1 and x=1/2 is the answer ?