Let $M$ be an upper triangular $n \times n$ matrix with entries only being 0 or 1 and having only ones on the diagonal. Let $N:=M + M^T$.
Question: Can the determinant and the inverse (in case it exists) of $N$ be explicitly described?
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See this question for some hints: https://math.stackexchange.com/questions/17776/inverse-of-the-sum-of-matrices – Anton Vrdoljak Jan 29 '20 at 08:58
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1The examples for dim. 4 show that values of determinant can be from the set 16,12, 8, 6, 5, 4... All depends on number and position of 1's. Interestingly that it seems that the determinant is always positive and $\le 16$ – Widawensen Jan 29 '20 at 15:44