Q116 / 180 · KCET 2015 · Mathematics

If \( \mathrm{A}=\left[\begin{array}{ll}\alpha & 2 \\ 2 & \alpha\end{array}\right] \) and \( \left|\mathrm{A}^{3}\right|=27 \), then \( \alpha= \)

  • A
    \( \pm 1 \)
  • B
    \( \pm 2 \)
  • Correct answer
    C
    \( \pm \sqrt{7} \)
  • D
    \( 0 \pm \sqrt{5} \)

Solution

Given that $A=\left[\begin{array}{ll}\alpha & 2 \\ 2 & \alpha\end{array}\right]$ And $\left|A^{3}\right|=27=|A|^{3}$ $\Rightarrow|A|=3$ So, $|A|=\alpha^{2}-4=3$ $\Rightarrow \alpha^{2}=7 \Rightarrow \alpha=\pm \sqrt{7}$

Hence, the correct answer is option: 'C'.

Relevant Questions