Matrices & Determinants
Determinants
Grade Class 12

Question:

The value of an odd order determinant in which a<sub>ij</sub> + a<sub>ji</sub> = 0 ∀ i, j is -
(A) perfect square
(B) negative
(C) ± 1
(D) 0

Step-by-Step Solution

Key Concept: A determinant of an odd order skew-symmetric matrix is always zero.
Let A be the matrix of the determinant. The condition a<sub>ij</sub> + a<sub>ji</sub> = 0 implies a<sub>ji</sub> = -a<sub>ij</sub>, which means A is a skew-symmetric matrix. The determinant of a skew-symmetric matrix of odd order is always 0.
Correct Answer: (D)

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