Stochastic matrix

Algebra Level pending

Let \(M = (m_{i,j})_{1\leq i,j \leq n} \in M_{n}(\mathbb R) \). For any couple \( (i,j)\) we have \(m_{i,j} \geq 0\) and \(\sum_{j=1}^n m_{i,j} =1\) for \( i \in [|1,n|]\). Calculate the maximum value of \(\det(M)\)

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