A shirt appears black when illuminated with cyan light and black when illuminated with magenta light. Identify the primary pigments which have been imparted to the shirt
Magenta light doesn't exist. Light which appears as magenta only exists as a mixing of red light + blue light, perceived by us as magenta. Because we know that the magenta light was created by both blue and red, and the shirt appears black illuminated by it, this implies that the shirt absorbs both red and blue light. This means that its color must either be green or black. As for cyan light, cyan light DOES exist as a monochromatic color, and is in fact part of Hydrogen's emission spectrum. But, cyan light could also be comprised of a polychromatic mixture of green through blue light. This still doesn't give us any more information than the shirt is either green or black. Either all the pigments are a part of the shirt, forming black when viewed in full spectrum white light; or both yellow pigment and cyan pigment are comprising it, both of which mix to form green when viewed in full spectrum white light.
Black means it is absorbing the light instead of reflecting it. So find the wavelengths of the light that is being absorbed and then find what pigments absorb those wavelengths or frequencies. That will tell you what pigments were used.
