Suppose that the eigenvalues of matrix $A$ are 1, 2, 4. The determinant of $(A^{-1})^T$ is __________.

The determinant of a matrix equals the product of its eigenvalues:

Using standard properties of determinants:

1. $\det(A^{-1}) = \frac{1}{\det(A)} = \frac{1}{8} = 0.125$

2. $\det(M^T) = \det(M)$ for any square matrix $M$

Therefore:

Hence, the determinant is 0.125 (accepted range: 0.124 to 0.126).