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

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

Answer: 0.125 

Explanation: 

The eigenvalues of matrix $A$ are 1, 2, 4. 

Therefore, determinant of $A$, $|A|$ = product of the  eigenvalues of $A$ = 8. 

Now, $|A^{-1}| = \frac{1}{|A|} = \frac{1}{8}$. 

Hence, $|(A^{-1})^T| = |A^{-1}| = \frac{1}{8} = 0.125$.