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(A) For a square matrix $A$ of order $n=3$,the property of the adjoint matrix is $|\operatorname{Adj} A| = |A|^{n-1}$.Substituting $n=3$,we get $|\ope

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Both $I$ and $II$

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(A) For a square matrix $A$ of order $n=3$,the property of the adjoint matrix is $|\operatorname{Adj} A| = |A|^{n-1}$.Substituting $n=3$,we get $|\operatorname{Adj} A| = |A|^{3-1} = |A|^2$.If $|A|=0$,then $|\operatorname{Adj} A| = 0^2 = 0$. Thus,statement $I$ is true.For statement $II$,we know that $A \cdot A^{-1} = I$,where $I$ is the identity matrix.Taking the determinant on both sides,$|A \cdot A^{-1}| = |I|$.Using the property $|AB| = |A||B|$,we get $|A| \cdot |A^{-1}| = 1$.Since $|A| 
eq 0$,we can divide by $|A|$,resulting in $|A^{-1}| = \frac{1}{|A|} = |A|^{-1}$. Thus,statement $II$ is true.Therefore,both statements $I$ and $II$ are correct.

If $A$ is a square matrix of order $3$,then consider the following statements.
$I$. If $|A|=0$,then $|\operatorname{Adj} A|=0$
$II$. If $|A| \neq 0$,then $|A^{-1}|=|A|^{-1}$
Which of the above statements is/are true?

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If $A$ is a square matrix of order $3$,then consider the following statements.$I$. If $|A|=0$,then $|\operatorname{Adj} A|=0$$II$. If $|A| \neq 0$,then $|A^{-1}|=|A|^{-1}$Which of the above statements is/are true?