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 $
$ |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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