Yes, that's the right key!
You can't really see the zoom history, like you can with the Undo History. But Inkscape remembers, up to a point.
Try this.
- Open a new blank file in Inkscape. (For some odd reason, new blank files open at 35% zoom.)
- Draw something simple, like a star, using the Star tool
- Change the zoom to 100%, by pressing the 1 key.
- Notice what happened to the star (or whatever). That's the size it would be if you uploaded the image to the internet, or printed it.
- Now change the zoom to 50% (by pressing the 2 key) and notice what happened to the star. You can see what the zoom level is by looking in the bottom, right corner of the window. See attachment. It should say 50%.
- Press `. Now it should show 100%, which is the zoom you were at before you changed to 50%.
- Press ` again, and it should go back to 35%.
- Press Shift ` and it should go to 100% again.
- Etc.
The reason I say Inkscape remembers up to a point, is because in my experience, after you go back a few steps, and forward a few steps, and back and forward, Inkscape seems to become sort of confused. After a while, it goes back almost to where it was before, but not exactly where it was before. But still a helpful feature, even if it still needs a little polishing.
I'm not sure what you are showing in the image you posted.... Oh....do you want the actual size of the drawing to change? Zooming makes you closer and farther away from your drawing. Closer so you can see tiny details much more clearly. Or further away, so you can see how it looks from further away. But the size of the drawing really never changes. If you save the drawing at 20% zoom, it will still save the 100% size drawing.
If you are trying to change the actual size of a drawing or object, you need to use some other tools.
By the way, it looks like you might be using an older version of Inkscape. If the ` key still isn't changing the zoom, maybe it wasn't available in that version.