The value of an odd order determinant in which a<sub>ij</sub> + a<sub>ji</sub> = 0 ∀ i, j is -
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)