1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# If $A=\left[\begin{array}{cc}\alpha & 2\\ \alpha & 2\end{array}\right]$ & $\left|{A}^{3}\right|=125$ then the value of $\mathbit{\alpha }$ is

A

$±1$

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

$±2$

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

$±3$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D

$±5$

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is C $±3$Explanation for the correct otpion:Finding the value of $\mathbit{\alpha }$:Given, $A=\left[\begin{array}{cc}\alpha & 2\\ 2& \alpha \end{array}\right]$ & $\left|{A}^{3}\right|=125$Now, $\left|A\right|={\alpha }^{2}-4$ &$\begin{array}{rcl}\left|{A}^{3}\right|& =& 125\\ \left|A\right|& =& 5\end{array}$Therefore, $5={\alpha }^{2}-4\phantom{\rule{0ex}{0ex}}9={\alpha }^{2}\phantom{\rule{0ex}{0ex}}\alpha =±3$Hence, correct option is $\mathbf{\left(}\mathbit{C}\mathbf{\right)}$

Suggest Corrections
23
Join BYJU'S Learning Program
Related Videos
Evaluation of Determinants
MATHEMATICS
Watch in App
Join BYJU'S Learning Program