I’m currently looking into Gentoo Linux. However I’m not very proficient in regards to laws. I’d like to knows the effective way to make my own operating system without having to make it open source. If possible, I’d love to see the statement that declared so in the official document too.
If you are looking to modify the source code for an OS without revealing your source code changes, then you cannot use Linux. The GPL license they use requires you to make your source code available to anyone receiving your changed software.
(Well, you can make changes for yourself only, but you cannot distribute copies, or ship products containing that modified code.)
You would need an open-source OS with a more permissive license. The obvious choice is BSD.
They welcome contributed changes that might be an improvement to BSD, but you are not obligated to contribute back to the project nor to provide source code to those receiving your software.