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