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Matrices (p-1) — Maths (commerce) STD 12 Commerce / Arts — Question

Maharashtra BoardEnglish MediumSTD 12 Commerce / ArtsMaths (commerce)Matrices (p-1)1 Mark
MCQ
If $A =\left[\begin{array}{ll}\alpha & 4 \\ 4 & \alpha\end{array}\right]$ and $\left| A ^3\right|=729$ then $\alpha=$
  • A
    \pm 3
  • B
    \pm 4
  • ✓
    \pm 5
  • D
    \pm 6
✓

Answer

Correct option: C.
\pm 5
(C) \pm 5
Hint:
$
\begin{aligned}
& | A |=\left|\begin{array}{ll}
\alpha & 4 \\
4 & \alpha
\end{array}\right|=\alpha^2-16 \\
& \therefore\left| A ^3\right|=| A |^3=\left(\alpha^2-16\right)^3=729 \\
& \therefore \alpha^2-16=9 \\
& \therefore \alpha^2=25 \\
& \therefore \alpha= \pm 5
\end{aligned}
$

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