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Let A be an n×n nonsingular matrix. Denote by adj(A) the adjugate matrix of A. Prove:...

Let A be an n×n nonsingular matrix. Denote by adj(A) the adjugate matrix
of A. Prove:
1)   det(adj(A)) = (det(A))

2)    adj(adj(A)) = (det(A))n−2A

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