GATE | GATE-CS-2016 (Set 2) | Question 16

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

[This Question was originally a Fill-in-the-blanks Question]

(A) 1/8
(B) 1
(C) 1/4
(D) 2


Answer: (A)

Explanation: Answer: 1/8
Determinant of A = 1*4*2 = 8 which is product of Eigen values.
Determinant of A-1 = 1/8 as determinant of inverse of matrix is inverse of determinant.
Determinant of Transpose (A-1) = 1/8 since determinant of transpose of matrix remains same as original one.

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