The square matrix $A =[a_{ij}]$ given by $a_{ij} = (i-j)^3$, is a

symmetric matrix skew-symmetric matrix diagonal matrix hermitian matrix

skew-symmetric matrix

We have, $a_{ij} = (i-j)^3⇒a_{ij} =(j-i)^3=-(i-j)^3=-a_{ij}$ for all i, j ∴ A is a skew-symmetric matrix.