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Determinants — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDeterminants1 Mark
MCQ
If $|A|=2$, where $A$ is a $2 \times 2$ matrix, then $\left|4 A^{-1}\right|$ equals:
  • A
    4
  • B
    2
  • C
    8
  • D
    $\frac{1}{32}$
✓

Answer

Given, $|A|=2$, Where $A$ is a $2 \times 2$ matrix.
Now, $\left|4 A^{-1}\right|=4|A|^{-1}$
and we know that, $|A|^{-1}=\frac{1}{|A|}$
$
\therefore\left|4 A^{-1}\right|=4 \times \frac{1}{|A|}=4 \times \frac{1}{2}=2
$

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