I have created a new web part page and added a document library to that page. In the ribbon the "Edit Properties" icon is enabled and I can edit the document properties.
When I add another web part to the page and go back to select a document, on the ribbon the "Edit Properties" icon is no disabled. I can still edit the document using the context menu of the document.
Permissions on the library did not change when I added the additional web part. The only change to the page was adding an additional web part.
View Complete Post