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
So, determinant of $(A^{-1})^T$ = $\text{det}(A^{-1}) = \frac{1}{8}$ = 0.125