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> Let $P$ and $Q$ be two stochastic matrices. Does the product $PQ$ have to be stochastic? Prove or disprove.
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What Im thinking is that since matrix multiplication is only defined for two matrices $A$ and $B$ where $A$ has the same amount of columns as $B$ has rows and vice versa. Therefore the product of any two stochastic matrices $P$ and $Q$ can not be stochastic. This is not much of a proof though.