Let A be a 2 times 2 matrix.Statement-1: adj( | vedclass

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(C) For any $n 	imes n$ matrix $A$,the property of the adjoint is $adj(adj A) = |A|^{n-2} A$.Given $n = 2$,we have $adj(adj A) = |A|^{2-2} A = |A|^0

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$Statement-1$ is true,$Statement-2$ is true; $Statement-2$ is a correct explanation for $Statement-1$

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(C) For any $n 	imes n$ matrix $A$,the property of the adjoint is $adj(adj A) = |A|^{n-2} A$.Given $n = 2$,we have $adj(adj A) = |A|^{2-2} A = |A|^0 A = I \cdot A = A$. Thus,$Statement-1$ is true.For $Statement-2$,we know that $|adj A| = |A|^{n-1}$.Given $n = 2$,we have $|adj A| = |A|^{2-1} = |A|^1 = |A|$. Thus,$Statement-2$ is true.Since $adj(adj A) = |A|^{n-2} A$,the result $adj(adj A) = A$ depends on the property $|A| = 1$ or the general identity for $n=2$. However,the standard property $adj(adj A) = |A|^{n-2} A$ is the fundamental reason why $adj(adj A) = A$ for $n=2$. Therefore,$Statement-2$ provides the necessary context for the identity in $Statement-1$.

Let $A$ be a $2 \times 2$ matrix.
$Statement-1: adj(adj A) = A$
$Statement-2: |adj A| = |A|$

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Let $A$ be a $2 \times 2$ matrix.$Statement-1: adj(adj A) = A$$Statement-2: |adj A| = |A|$