Let \( A \) be a \( 3 \times 3 \) non-singular matrix such that \( |A| = 4 \). If \( B = \text{adj}(2A) \), then the determinant \( |B| \) is equal to:

For an \( n \times n \) matrix, \( |\text{adj}(kA)| = |k^{n-1} \text{adj}(A)| = (k^{n-1})^n |\text{adj}(A)| = k^{n(n-1)} |A|^{n-1} \). For \( n=3 \), \( k=2 \), and \( |A|=4 \), \( |\text{adj}(2A)| = 2^{3(2)} \cdot 4^{3-1} = 2^6 \cdot 4^2 = 64 \times 16 = 1024 \).