How to prove that adj(kA) = K^(n-1).adj(A)?

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If A is a square matrix of order n xx n and k is a scalar, then adj (kA) is equal to (1) k adj A... If A is a square matrix of order n xx n and k is a scalar, then adj (kA) is equal to (1) k adj A...
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How to prove that adj(adj(A))=(det(A))^(n-2).A? How to prove that adj(adj(A))=(det(A))^(n-2).A?