Chapter 7 - Eigenvalues and Eigenvectors - 7.3 Symmetric Matrices and Orthogonal Diagonalization - 7.3 Exercises - Page 370: 1

symmetric

A matrix is symmetric if it is equal to its transpose. Here the transpose of the matrix is $\begin{bmatrix} 1& 3 \\ 3& -1\\ \end{bmatrix} $, which is the same as the original matrix; thus it is symmetric.