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I need to either prove or disprove by a counterexample the following proposition:

" Let A be an m by n row-stochastic matrix in which all entries are positive real numbers and let B be an n by m column-stochastic matrix with the same feature. Then all eigen values of the m by m matrix AB are real."

Can anyone help? It may be noted that AB is not necessarily symmetric (Hermitian).

" Let A be an m by n row-stochastic matrix in which all entries are positive real numbers and let B be an n by m column-stochastic matrix with the same feature. Then all eigen values of the m by m matrix AB are real."

Can anyone help? It may be noted that AB is not necessarily symmetric (Hermitian).

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