# 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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