Answer
Since A = $A^{T}$, the matrix is 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 = $\begin{bmatrix}
-6 & 2 & 0 \\
2 & -6 & 2\\
0 & 2 & -6
\end{bmatrix}$ $A^{T}$=$\begin{bmatrix}
-6 & 2 & 0 \\
2 & -6 & 2\\
0 & 2 & -6
\end{bmatrix}$
Since A = $A^{T}$, the matrix is symmetric.