The "Hue" Is the Colour, Independent of Brightness and How

Essay

The "hue" is the colour, independent of brightness and how much pure white has been added to it. We can make a simple definition of hue as the set of ratios R:G:B. Suppose a colour (i.e., an RGB) is divided by 2.0, so that the RGB triple now has values 0.5 times its former values. Explain using numerical values:
(a) If gamma-correction is applied after the division by 2.0 and before the colour is stored, does the darker RGB have the same hue as the original in the sense of having the same ratios R:G:B of light emanating from the CRT display device? (we're not discussing any psychophysical effects that change our perception - here we're just worried about the machine itself).
(b) If gamma-correction is not applied, does the second RGB have the same hue as the first RGB, when displayed?
(c) For what colour triples is the hue always unchanged?