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Cofactor Matrix of Cofactor Matrix

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A* adj(A) = det(A)I => det(adj(A)) = det(A)^(n-1).

Now adj(A)* adj(adj(A)) = det(adj(A))I

=> adj(adj(A)) = det(adj(A))* A/det(A)
by uniqueness of matrix inverse (at least for det(A) != 0)
= A* det(A)^(n-2)
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I think it’s scaled by detA*det(adjA). The formula for the inverse of A is (1/detA)*adjA, where adjA is the cofactor matrix.

So doing this again would be 1/(det(adjA))*1/detA*adj(adjA), which is equal to the original matrix A. Then adj(adj(A)) = detA*det(adjA)*A

Hopefully everything is correct here, I’m answering on mobile
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