If \(A = [a_{ij}]\) is a square matrix of odd order such that \(a_{ij} = i^2 - j^2\), then
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → A is a skew-symmetric matrix
Interchanging i and j in the rule:
\( a_{ji} = j^2 - i^2 = -(i^2 - j^2) = -a_{ij} \)
So \(A' = -A\), and A is skew-symmetric. As in every skew-symmetric matrix, the diagonal entries are \(a_{ii} = i^2 - i^2 = 0\).
The entry \(a_{12} = 1 - 4 = -3\) is not zero and \(a_{21} = 3 \ne a_{12}\), so A is not a null matrix, not the identity matrix and not symmetric.