A=matrix(QQ,[[4,1,0,2], [-1,3,5,1], [0,1,4,0],[2,-1,-1,1]])
B=matrix(QQ,[[1,2,3,4,5],[5,4,3,2,1],[2,1,3,5,4],[9,5,7,1,5],[2,1,1,5,1]])
C=matrix(QQ,[[4,1,0,2,6,8], [-1,3,5,1,1,5], [0,1,4,0,1,5],[2,-1,-1,1,1,5],[6,5,1,2,5,1],[1,6,8,8,7,6]])
print "det(adj A)= ",A.adjoint().det()
print "(det A)^(n-1)",A.det()^(3)
print "det(adj B)= ",B.adjoint().det()
print "(det B)^(n-1)",B.det()^(4)
print "det(adj C)= ",C.adjoint().det()
print "(det C)^(n-1)",C.det()^(5)
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det(adj A)= 27000
(det A)^(n-1) 27000
det(adj B)= 429981696
(det B)^(n-1) 429981696
det(adj C)= 14808575318291015625
(det C)^(n-1) 14808575318291015625
det(adj A)= 27000
(det A)^(n-1) 27000
det(adj B)= 429981696
(det B)^(n-1) 429981696
det(adj C)= 14808575318291015625
(det C)^(n-1) 14808575318291015625
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