Question:

Step 1: Recall the property of determinants for a transpose matrix. A fundamental property of determinants states that the determinant of a matrix is equal to the determinant of its transpose. This can be expressed as: $$ \det(A^T) = \det(A) $$ Step 2: Substitute the given value of $\det(A)$. We are given that $\det(A) = -4$. Using the property from Step 1, we can substitute this value: $$ \det(A^T) = -4 $$ Step 3: State the final answer and match the option. The value of $\det(A^T)$ is $-4$. The final answer is $\boxed{-4}$. This corresponds to Option 1.