If $A = [a_{ij}]$ is a square matrix of even order such that $a_{ij}=i^2-j^2$, then

A is a skew-symmetric matrix and $|A|=0$ A is symmetric matrix and $|A|$ is a square A is symmetric matrix and $|A|=0$ none of these

none of these

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.