How is the determinant of a determinant equal to the determinant of the matrix to the power of its number of rows?

How is the following true?:

det((det(A))I) = (det(A))^n(det(I))=(det(A))^n

I understand that det((det(A))I) = det(det(A))det(I) and that the determinant of the Identity matrix is 1, but don't understand the relation that det(det(A))=(det(A))^n.
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