Answer
Since A $\ne$ $A^{T}$, the matrix is not symmetric.
Work Step by Step
The definition of a symmetric matrix is as follows a symmetric matrix is a matrix A such that $A^{T}$ = A. A symmetric matrix must be square.
A = $\begin{bmatrix}
0 & 8 & 3 \\
8 & 0 & -4\\
3 & 2 & 0
\end{bmatrix}$ $A^{T}$=$\begin{bmatrix}
0 & 8 & 3 \\
8 & 0 & 2\\
3 & -4 & 0
\end{bmatrix}$
Since A $\ne$ $A^{T}$, the matrix is not symmetric.