1. **Stating the problem:** Determine if the matrix $$\begin{bmatrix}1 & 5 \\ 5 & 1\end{bmatrix}$$ is symmetric. 2. **Definition of symmetric matrix:** A matrix is symmetric if it is equal to its transpose, that is, $$A = A^T$$ 3. **Find the transpose of the matrix:** The transpose is obtained by swapping rows and columns: $$A^T = \begin{bmatrix}1 & 5 \\ 5 & 1\end{bmatrix}$$ 4. **Compare the original matrix and its transpose:** Here, $$A = \begin{bmatrix}1 & 5 \\ 5 & 1\end{bmatrix}, \quad A^T = \begin{bmatrix}1 & 5 \\ 5 & 1\end{bmatrix}$$ Since the matrix equals its transpose, $$A = A^T$$ 5. **Conclusion:** Matrix 14 is symmetric. Final answer: Matrix $$\begin{bmatrix}1 & 5 \\ 5 & 1\end{bmatrix}$$ is symmetric.