Can the Pigeonhole Principle Solve This Combinatorics Problem?

[LineIntegral]

Homework Statement

Let A be a 100x100 matrix such that each number from the set {1,2,...,100} appears exactly 100 times. Prove that there exists a row or column with at least 10 different numbers.

Homework Equations

The Attempt at a Solution

I suspect that I should use the pigeonhole principle, but I can't think of a way to do so.

 

[lanedance]

so as a start could you look for a contradiction by assuming every row & column can have 9 or less distinct numbers

 

[LineIntegral]

Solved it, thanks :)