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.
$A=\begin{bmatrix}
3 & 5 \\
5 & -7
\end{bmatrix}$ $A^{T}=\begin{bmatrix}
3 & 5 \\
5 & -7
\end{bmatrix}$
Since $A=A^{T}$, the matrix is symmetric.