## Differential Equations and Linear Algebra (4th Edition)

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