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If $A$ is a square matrix, then $A+A^{\top}$ is
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Symmetric matrix
$A+A^T$ is a square matrix.
$\left(A+A^T\right)^T=A^T+\left(A^T\right)^T=A^T+A$
Hence $A$ is a symmetric matrix.
$\left(A+A^T\right)^T=A^T+\left(A^T\right)^T=A^T+A$
Hence $A$ is a symmetric matrix.
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