If A is a 3 times 3 matrix and |A|=2,then |3 | vedclass

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(A) Given $A$ is a $3 	imes 3$ matrix,so $n=3$ and $|A|=2$. First,calculate $|3A|$. Since $A$ is $3 	imes 3$,$|3A| = 3^3 |A| = 27 	imes 2 = 54$. No

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$3^{11} \cdot 6^{10}$

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(A) Given $A$ is a $3 	imes 3$ matrix,so $n=3$ and $|A|=2$. First,calculate $|3A|$. Since $A$ is $3 	imes 3$,$|3A| = 3^3 |A| = 27 	imes 2 = 54$. Now,we need to find $|3 \operatorname{adj}(|3A|A^2)| = |3 \operatorname{adj}(54A^2)|$. Using the property $|kM| = k^n |M|$ for an $n 	imes n$ matrix $M$,we have $|3 \operatorname{adj}(54A^2)| = 3^3 |\operatorname{adj}(54A^2)| = 27 |\operatorname{adj}(54A^2)|$. Using the property $|\operatorname{adj}(M)| = |M|^{n-1}$,we get $27 |54A^2|^{3-1} = 27 |54A^2|^2$. Since $|54A^2| = 54^3 |A^2| = 54^3 |A|^2 = 54^3 	imes 2^2 = 54^3 	imes 4$. Substituting this back: $27 	imes (54^3 	imes 4)^2 = 27 	imes 54^6 	imes 16 = (3^3) 	imes (2 	imes 3^3)^6 	imes 2^4 = 3^3 	imes 2^6 	imes 3^{18} 	imes 2^4 = 3^{21} 	imes 2^{10} = 3^{11} 	imes 3^{10} 	imes 2^{10} = 3^{11} 	imes (3 	imes 2)^{10} = 3^{11} 	imes 6^{10}$.

If $A$ is a $3 \times 3$ matrix and $|A|=2$,then $|3 \operatorname{adj}(|3A|A^2)|$ is equal to $.........$.

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