Let P = [a_{ij}] be a 4 times 4 matrix. If |P | vedclass

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(D) Given that $P$ is a $4 	imes 4$ matrix,so $n = 4$.We know that for any $n 	imes n$ matrix $A$,$|adj(A)| = |A|^{n-1}$.Here,$A = 3P$,so $|adj(3P)|

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None of these

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(D) Given that $P$ is a $4 	imes 4$ matrix,so $n = 4$.We know that for any $n 	imes n$ matrix $A$,$|adj(A)| = |A|^{n-1}$.Here,$A = 3P$,so $|adj(3P)| = |3P|^{4-1} = |3P|^3$.Since $P$ is a $4 	imes 4$ matrix,$|3P| = 3^4 |P|$.Substituting the value of $|P| = -2$,we get $|3P| = 3^4 	imes (-2) = -2 \cdot 3^4$.Now,$|adj(3P)| = (-2 \cdot 3^4)^3 = (-2)^3 \cdot (3^4)^3 = -8 \cdot 3^{12} = -3^{12} \cdot 2^3$.Comparing this with the given options,none of the options match the result $-3^{12} \cdot 2^3$.

Let $P = [a_{ij}]$ be a $4 \times 4$ matrix. If $|P| = -2$,then the value of $|adj(3P)|$ is (where $|A|$ denotes the determinant value of matrix $A$).

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