If the determinant of the adjoint of a (real) | vedclass

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(D) Given,the determinant of the adjoint of a (real) matrix $A$ of order $n=3$ is $|\operatorname{adj} A| = 25$. We know the property $|\operatorname{

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$\pm 0.2$

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(D) Given,the determinant of the adjoint of a (real) matrix $A$ of order $n=3$ is $|\operatorname{adj} A| = 25$. We know the property $|\operatorname{adj} A| = |A|^{n-1}$. Substituting $n=3$,we get $|\operatorname{adj} A| = |A|^{3-1} = |A|^2$. Thus,$|A|^2 = 25$,which implies $|A| = \pm 5$. We need to find the determinant of the inverse of the matrix,which is $|A^{-1}|$. Using the property $|A^{-1}| = \frac{1}{|A|}$,we get $|A^{-1}| = \frac{1}{\pm 5} = \pm 0.2$.

If the determinant of the adjoint of a (real) matrix of order $3$ is $25$,then the determinant of the inverse of the matrix is

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