PE-MO 2021 Problem 2

The numbers $1$ to $25$ will be written in a table $5 \times 5$ . First, Ana chooses $k$ of these numbers( $1$ to $25$ ), and write in some cells. Then, Enrique writes the remaining numbers with the following goal: The product of the numbers in some column/row is a perfect square.a) Prove that if $k=5$ , Ana can avoid Enrique to reach his goal.b) Prove that if $k=4$ , Enrique can reach his goal.