1997 AHSME Problem 16

The three row sums and the three column sums of the array

\left[\begin{matrix}4 & 9 & 2\\ 8 & 1 & 6\\ 3 & 5 & 7\end{matrix}\right]

are the same. What is the least number of entries that must be altered to make all six sums different from one another?

\textbf{(A)}\ 1\qquad\textbf{(B)}\ 2\qquad\textbf{(C)}\ 3\qquad\textbf{(D)}\ 4\qquad\textbf{(E)}\ 5

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.