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

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

JEE MainJEE Main 2015Determinants

Solution:

Order of $A$ is $3 \times 3 ;|5\,. adj\, A|=5$;
$|5(adj A)|=5 \Rightarrow (5)^{3}|Adj . A|=5$
$\Rightarrow (5)^{2}| A |^{\beta-1}=1$
$\Rightarrow |A|^{2}=\frac{1}{25}$
$\Rightarrow |A|=\pm \frac{1}{5}$