Matrices & Determinants
Skew-symmetric matrix
Grade Class 12
Question:
The value of an odd order determinant in which a<sub>ij</sub> + a<sub>ji</sub> = 0 for all i, j is -
(A) perfect square
(B) negative
(C) ± 1
(D) 0
Step-by-Step Solution
Key Concept: A determinant of a skew-symmetric matrix of odd order is always zero.
Given a<sub>ij</sub> + a<sub>ji</sub> = 0, which implies a<sub>ji</sub> = -a<sub>ij</sub>. This is the definition of a skew-symmetric matrix. The determinant of a skew-symmetric matrix of odd order is always 0.
Correct Answer: 4