Let $A = [a_{ij}]_{n \times n}$ where $a_{ij} = i^2 - j^2$. Then $A$ is
Step-by-Step Solution
Key Concept: A matrix is skew-symmetric if its elements satisfy $a_{ij} = -a_{ji}$ for all $i, j$, which is verified here as $i^2 - j^2 = -(j^2 - i^2)$.
<div>$A = \begin{bmatrix} 1^2-1^2 & 1^2-2^2 & 1^2-3^2 \\ 2^2-1^2 & 2^2-2^2 & 2^2-3^2 \\ 3^2-1^2 & 3^2-2^2 & 3^2-3^2 \end{bmatrix} = \begin{bmatrix} 0 & -3 & -8 \\ 3 & 0 & -5 \\ 8 & 5 & 0 \end{bmatrix}$<br>So $A$ is skew symmetric matrix.</div>
Correct Answer: C