Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
OK, in graph theory that would be a $2 \times 2$ grid graph. Now for your $n=2$, that would have $9$ nodes and $12$ edges, and you are claiming that removing $2^2-2+1=3$ edges can eliminate all rectangles. What is a rectangle, and which $3$ edges do you remove?