Determinant of Matrix $A =$ product of eigen values $= 1 \times 2 \times 4 =8$
Determinant of Inverse Matrix of $A, \text{det}(A^{-1}) = \frac{1}{\text{det}(A)} =\frac{1}{8}$
Determinant remains same after the Transpose operation.
So, determinant of $(A^{-1})^T = \text{det}(A^{-1}) = \frac{1}{8} = 0.125$