Explanation:

- The determinant of a matrix A is a scalar value reflecting the volume change under the linear transformation depicted by A.

- For a 3x3 matrix A, the formula for the determinant of the adjugate (adjoint) of A, denoted as Adj. A, is given by: det(Adj. A) = (det A)².

- Given that det A = 4, calculate det(Adj. A) as (4)² = 16.

- ? Option 3: 16 is the correct answer.

- Det(Adj. A) equals 16, derived from the fact that Adj. A involves cofactor expansion where each cofactor itself has been multiplied by the determinant of the matrix up to the (n-1)th power for an n x n matrix.