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

GATE 2016 · Engineering Mathematics · Eigen Value · medium

Answer: 0.125

1. Compute det(A) from eigenvalues: det(A) = 1 * 2 * 4 = 8.
2. Apply determinant of inverse property: det(A^(-1)) = 1/8 = 0.125.
3. Apply determinant of transpose property: det((A^(-1))^T) = det(A^(-1)) = 1/8 = 0.125.