Chapter 2 - Matrices and Systems of Linear Equations - 2.1 Matrices: Definitions and Notation - Problems - Page 122: 26

$\begin{bmatrix} 0 & 0 & 0\\ 0 & 0 & 0\\ 0 & 0 & 0\\ \end{bmatrix}$

$a_{ji}=a_{ij}~and~a_{ji}=-a_{ij}$. That is, $a_{ij}=-a{ij}$. We can conclude that: $a_{ij}=0$ The only possibility is: $\begin{bmatrix} 0 & 0 & 0\\ 0 & 0 & 0\\ 0 & 0 & 0\\ \end{bmatrix}$