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Determinantseasy
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Which of the following statements about the adjugate (adjoint) matrix adj(A)\text{adj}(A)adj(A) are true for any invertible n×nn \times nn×n matrix AAA?

I. A⋅adj(A)=det⁡(A)⋅IA \cdot \text{adj}(A) = \det(A) \cdot IA⋅adj(A)=det(A)⋅I

II. A−1=1det⁡(A)adj(A)A^{-1} = \frac{1}{\det(A)} \text{adj}(A)A−1=det(A)1​adj(A)

III. det⁡(adj(A))=(det⁡(A))n−1\det(\text{adj}(A)) = (\det(A))^{n-1}det(adj(A))=(det(A))n−1