Let \(A\) be a square matrix with real entries such that \[ A A^T+A^T A = A+A^T.\] Prove that \(A\) and \(A^T\) have the same column space.
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2016-16 Column spaces,
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Let \(A\) be a square matrix with real entries such that \[ A A^T+A^T A = A+A^T.\] Prove that \(A\) and \(A^T\) have the same column space.