Hello, Cropping is a document-wide action.
You might want to do a selection with the marquee tool, and either invert the selection (CTRL+Shift+I on a Pc or Command+Shift+I on a Mac) and delete the outer area, or better, select then click on the add layer mask on the layer panel.
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Yeah, it took me awhile to get my head around it when I first started. As PECourtejoie stated cropping is for the whole document.
For a single layer just use the square selection tool, drag out the area you want in the new layer, then hit ctrl-j it will copy that area into a new layer for you.
If you want the selection to fill the thumbnail, just right click on the thumbnail, at the bottom of the menu you will find clip to layer bounds. Once that is selected the selection will fill the thumbnail.
Note that if you do my first suggestion or Silkrooster's, there is no way to go back, or change what area is displaying. You need to duplicate the layer and hide it in my case, or hide the layer in Silkrooster's, then start again. With the layer mask solution, you can unlink it, and move the layer mask, and therefore, the area that is showing. It is called non-destructive editing.
Thank you both very much for the help. THis behaviour isn't shared by Final Cut and After Effects. Very grateful.