Where can I find manual solution for textbooks like Advanced Linear Algebra by Rotman or Introduction to Smooth manifolds by Lee? any help would be appreciated
Sometimes, publishers will sell (or send for free) solutions manuals to problems in their textbooks if you are a teacher that is using the textbook in class. They might ask for proof of this (for example, a class webpage listing the textbook as the reference with your name as the teacher). (This happened to me a few decades ago---a probability textbook by Peebles from McGraw-Hill.) Visit the publisher's website or contact the publisher directly to find out if they have such a manual available.
Of course, some authors do not create solutions manuals for their textbooks. There is a chance that someone else has created such a manual (for example, I know a faculty member who did this). You might find these by using an internet search engine. But be careful in this case because you would not be sure if the solutions are correct.
I assume you mean roman not rotman.