If A is a 3 times 3 matrix such that |5 cdot | vedclass

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(A) Given that $A$ is a $3 	imes 3$ matrix,so $n = 3$.We know the property $|k \cdot M| = k^n |M|$,where $M$ is an $n 	imes n$ matrix.Applying this

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$\pm \frac{1}{5}$

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(A) Given that $A$ is a $3 	imes 3$ matrix,so $n = 3$.We know the property $|k \cdot M| = k^n |M|$,where $M$ is an $n 	imes n$ matrix.Applying this to the given equation: $|5 \cdot 	ext{adj } A| = 5^3 |	ext{adj } A| = 125 |	ext{adj } A|$.We also know the property $|	ext{adj } A| = |A|^{n-1}$.Substituting $n = 3$,we get $|	ext{adj } A| = |A|^{3-1} = |A|^2$.Therefore,the equation becomes $125 |A|^2 = 5$.$|A|^2 = \frac{5}{125} = \frac{1}{25}$.Taking the square root on both sides,$|A| = \pm \sqrt{\frac{1}{25}} = \pm \frac{1}{5}$.

If $A$ is a $3 \times 3$ matrix such that $|5 \cdot \text{adj } A| = 5$,then $|A|$ is equal to

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