If $A = [a_{ij}]$ is a square matrix of even order such that $a_{ij}=i^2-j^2$, then
Answer & explanation
Correct answer: option 4
We have, $a_{ij}=i^2-j^2$
$∴a_{ji} = j^2-i^2 ⇒ a_{ij} = - a_{ji}$
Thus, A is a skew-symmetric matrix of even order.
We know that the determinant of every skew-symmetric matrix of even order is a perfect square and that of odd order is zero.
Hence, option (4) is correct.