There are many different ways to Undo in Photoshop. Ctrl + Z is keyboard shortcut for Undo last operation, Ctrl + Alt + Z is Undo keyboard shortcut. You can Undo and from Edit > Undo or from HISTORY panel (Window > History).
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Or, Image>Adjustments>Invert
Curves is adjustment in Photoshop where you can adjust colors and tones in an image.
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Image > Adjustments > Match Color
The app that shows colors in a picture is Photoshop.
Black as the foreground, and White as the background. I have seen blue appear as the foreground. You can change these colours to every colour of the spectrum and beyond. As far as I can see, there is no way to change the default colors.
Photoshop does not have library as InDesign for example, answer can be nothing, library is nothing in Photoshop. Other programs have libraries where you can put shapes for example to re use them. In Photoshop you can say brush library or swatches, colors library.
Smooth transition between two or more colors.
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Gamut represents all possible colors in that particular color space.
Open image. At top of screen, click IMAGE>MODE>RGB.
You mean Color Mode? Changing how Photoshop treats and displays colors in an image.