2017-12 Invertible matrices

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

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2017-12 Invertible matrices, 2.8 out of 5 based on 19 ratings