2024 AMC 8 Problem 16

Minh enters the numbers 1 through 81 into the cells of a 9 \times 9 grid in some order. She calculates the product of the numbers in each row and column. What is the least number of rows and columns that could have a product divisible by 3?

\textbf{(A)} 8 \qquad \textbf{(B)} 9 \qquad \textbf{(C)} 10 \qquad \textbf{(D)} 11 \qquad \textbf{(E)} 12

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