Works great for flying cats
If you want to give your cat free access into specific rooms without opening the door for them, just install one of these cute kitty doors. They’re pretty cheap and incredibly easy to install. Just take your door down, use the included template to draw the hole on your door, and cut it out with whatever power tool you have. A jig saw is the go-to tool for jobs like this.

Just make sure you put the template on the correct part of the door. The rule of thumb is to measure twice and cut once. However, make sure you take a step back to assess your work prior to cutting.