Let A be a nonsingular square matrix of order | vedclass

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(C) We know that for any square matrix $A$ of order $n$,the property of the adjoint matrix is given by: $A(adj\, A) = (adj\, A)A = |A|I_n$ Taking the

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$|A|^{2}$

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(C) We know that for any square matrix $A$ of order $n$,the property of the adjoint matrix is given by: $A(adj\, A) = (adj\, A)A = |A|I_n$ Taking the determinant on both sides: $|A(adj\, A)| = ||A|I_n|$ $|A| \cdot |adj\, A| = |A|^n \cdot |I_n|$ Since $|I_n| = 1$,we have: $|A| \cdot |adj\, A| = |A|^n$ $|adj\, A| = |A|^{n-1}$ Given that the order of the matrix $A$ is $3 	imes 3$,so $n = 3$. Therefore,$|adj\, A| = |A|^{3-1} = |A|^2$. Hence,the correct answer is $C$.

Let $A$ be a nonsingular square matrix of order $3 \times 3$. Then $|adj\, A|$ is equal to

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