2025 USA-NA-AIO Round 1, Problem 1, Part 3

Part 3 (10 points, non-coding task)

Explain why \mathbf{A} is a symmetric matrix.

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Because

\mathbf{A}^\top = \mathbf{A} = \begin{bmatrix} 1 & 1 \\ 1 & 0 \end{bmatrix} ,

matrix \mathbf{A} is symmetric.

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