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9 votes
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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  

  1. $\frac{1}{2}$
  2. $\sqrt2$
  3. $\pm \frac{1}{2}$
  4. $\pm \frac{1}{\sqrt2}$
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1 Answer

Best answer
13 votes
13 votes
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.

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