Let \(A\) and \(B\) be \(n\times n\) real matrices for an odd integer \(n\). Prove that if both \(A+A^T\) and \(B+B^T\) are invertible, then \(AB\neq 0\).
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Let \(A\) and \(B\) be \(n\times n\) real matrices for an odd integer \(n\). Prove that if both \(A+A^T\) and \(B+B^T\) are invertible, then \(AB\neq 0\).
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