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  4. If A is a 3 × 3 matrix such that mid 5 ⋅ adj A mid=5 then |A| is equal to

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Q. If $A$ is a $3 \times 3$ matrix such that $\mid 5 \cdot$ adj $A \mid=5$ then $|A|$ is equal to

KCETKCET 2022Determinants

Solution:

$A_{3 \times 3}$ matrix $|5 . \operatorname{AdjA}|=5$
$\Rightarrow 5^{3}| A |^{2}=5 $
$\Rightarrow\left| A ^{2}\right|=\frac{1}{5^{2}}$
$| A |=\pm \frac{1}{5}$