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3 and 4 . determinant and metrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths3 and 4 . determinant and metrices1 Mark
MCQ
Let $A = \left[ {\begin{array}{*{20}{c}}5&{5\alpha }&\alpha \\0&\alpha &{5\alpha }\\0&0&5\end{array}} \right]$, If ${\left| A \right|^2} = 25$, then $\left| \alpha \right|$ equals
  • ✓
    $\frac{1}{5}$
  • B
    $5$
  • C
    ${5^2}$
  • D
    $1$
✓

Answer

Correct option: A.
$\frac{1}{5}$
a
$\left|A^{2}\right|=25 \Rightarrow|A|^{2}=25$

$\Rightarrow(25 \alpha)^{2}=25 \Rightarrow|\alpha|=\frac{1}{5}$

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