Let A= [ lll 1 & 0 & 0 0 & & 0 & & ] and |2 A|^3=2^ 21 where , Z,… - Vidyadip

MCQ

Let $A=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & \alpha & \beta \\ 0 & \beta & \alpha\end{array}\right]$ and $|2 A|^3=2^{21}$ where $\alpha, \beta \in Z$, Then a value of $\alpha $ is

A
$3$
✓
$5$
C
$17$
D
$9$

✓

Answer

Correct option: B.

$5$

b
$ |A|=\alpha^2-\beta^2 $

$ |2 A|^3=2^{21} \Rightarrow|A|=2^4 $

$ \alpha^2-\beta^2=16 $

$ (\alpha+\beta)(\alpha-\beta)=16 \Rightarrow \alpha=4 \text { or } 5$

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