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NDA 2017
Exam
NDA
Year
2017
Subject
Mathematics
Chapter
Matrices

NDA 2017 · Mathematics · Matrices

If A=[ array cc α & 2 2 & α array ] and (A^3)=125 , then α is equal...

If A=\left[α22α\begin{array}{cc}\alpha & 2 \\ 2 & \alpha\end{array}\right] and\operatorname\det\left(A^3\right)=125,then, then\alpha is equal to

Options

  1. A±1\pm 1
  2. B±2\pm 2
  3. C±3\pm 3
  4. D±5\pm 5

Correct answer

C. ±3\pm 3

Step-by-step solution

A=[α22α],det⁡⁡(A3)=125∣A3∣=125⇒∣A∣=5∴α2−4=5⇒α2=9⇒α=±3\begin{aligned} & \mathrm{A}=\left[\begin{array}{ll}\alpha & 2 \\ 2 & \alpha\end{array}\right], \operatorname\det\left(\mathrm{A}^3\right)=125 \\ & \left|\mathrm{ A}^3\right|=125 \Rightarrow|\mathrm{ A}|=5 \\ & \therefore \alpha^2-4=5 \Rightarrow \alpha^2=9 \Rightarrow \alpha= \pm 3\end{aligned}
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