# Let A be an $m\times n$ payoff matrix of a two person zero sum game. If the avg entry in a column $\ge 5$. Show row player's expected winnings $\ge 5$

Let A be an $$m\times n$$ payoff matrix of a two person zero sum game. If the avg entry in a column$$\ge 5$$. Show that the row player's expected winnings $$\ge 5$$

I'm assuming the proof has to do with the fact that every index in the column has an avg of 5 or more so that probably means the rows have an average of 5 or more. So regardless of the what row player 1 chooses the avg expected reward will be at least 5 as well, but I'm not sure that's a complete proof.