Determine the maximin and minimax strategies for the two-person, zero-sum matrix game.
\[
\left[\begin{array}{rr}
-1 & 5 \\
5 & 7
\end{array}\right]
\]

The row player's maximin strategy is to play row
The column player's minimax strategy is to play column

Step 1 ：Given the two-person, zero-sum matrix game \(\left[\begin{array}{rr} -1 & 5 \ 5 & 7 \end{array}\right]\)

Step 2 ：The maximin strategy for the row player is to maximize the minimum payoff. This means the row player will look at the minimum value in each row and choose the row with the highest of these minimums.

Step 3 ：The minimax strategy for the column player is to minimize the maximum loss. This means the column player will look at the maximum value in each column and choose the column with the lowest of these maximums.

Step 4 ：The minimum payoff in each row is \([-1, 5]\). So, the maximin strategy for the row player is to play row 2, as the minimum payoff in this row (5) is higher than the minimum payoff in row 1 (-1).

Step 5 ：The maximum loss in each column is \([5, 7]\). So, the minimax strategy for the column player is to play column 1, as the maximum loss in this column (5) is lower than the maximum loss in column 2 (7).

Step 6 ：Final Answer: The maximin strategy for the row player is to play row 2. The minimax strategy for the column player is to play column 1. \(\boxed{2, 1}\).