Correct : 48

The correct answer is 48.
For any n×n matrix A, scaling the matrix by a scalar k scales the determinant by kⁿ. This is because each row of the matrix gets multiplied by k, and there are n rows - each contributing a factor of k to the determinant.
Formula: det(kA) = kⁿ · det(A)
Here, the matrix is 4×4 (n = 4), the scalar is k = 2, and det(A) = 3. Applying the formula:
det(2A) = 2⁴ × 3 = 16 × 3 = 48.
Why kⁿ and not just k? The determinant is a multilinear function of the rows (or columns). Multiplying the entire matrix by k multiplies every one of the n rows by k, so the determinant picks up a factor of k exactly n times - giving kⁿ, not k.
A common mistake is to compute 2 × 3 = 6 (forgetting the matrix dimension) or 2³ × 3 = 24 (using n−1). Always use the full dimension n in the formula.