Question

If $A=\left(\begin{array}{ccc}5& 5x& x\\ 0& x& 5x\\ 0& 0& 5\end{array}\right)$ and $|A^2|=25$, then $|x|$ is equal to

• A. $\frac{1}{5}$
• B. $5$
• C. $5^2$
• D. $1$

Answer 1

The correct option is A $\frac{1}{5}$

$A=\left[\begin{array}{ccc}5& 5x& x\\ 0& x& 5x\\ 0& 0& 5\end{array}\right]$

$|A|=25x$
$\Rightarrow |A{|}^2=625x^2$

$|A^2|=25$

We know that, $|A{|}^2=|A^2|$
$\Rightarrow 25={25}^2{x}^2$
$\Rightarrow |x|=\frac{1}{5}$