Really, in either case, it won't work, unfortunately.
The browser is a very basic function and can't support media content.
The app, if even loaded on your tv, won't work. If you have a later software version, the app isn't there at all.
The reason for this is that samsung ended its marketing agreement with amazon for all 2012 and prior model tvs. Your is a 2011 model and was included in this change. What that means is that it is not possible to access the amazon instant video app/services directly on this tv. This is a common problem with smart tvs as manufacturers have to publish a specific app for every individual tv model, and they eventually stop supporting them because of costs. So it is not possible to use amazon on the tv directly.
You can still do so, but would need to use an external streaming device such as a roku, roku4k, fire tv, htpc or smart bluray player and get all the same functions and many more, with better performance and support.
Best regards, ***** ***** for the news,