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Determinantshard
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For an invertible matrix AAA, the fundamental relationship A⋅adj(A)=det⁡(A)⋅IA \cdot \text{adj}(A) = \det(A) \cdot IA⋅adj(A)=det(A)⋅I holds, where adj(A)\text{adj}(A)adj(A) is the adjugate (classical adjoint) matrix. If det⁡(A)=4\det(A) = 4det(A)=4 and the (2,1)(2,1)(2,1)-entry of adj(A)\text{adj}(A)adj(A) is 8, what is the (2,1)(2,1)(2,1)-entry of A−1A^{-1}A−1?