Colour and intensity of light

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In the opponent processes model of Jameson and Hurvich for seeing colours, the signals of the L, M, and S-cones in the retina are re-encoded into a signal with also three values by taking linear combinations of the activities of the cones. The image of $(L,M,S)$ -coordinates to the new $(A,RG, Y\!B)$ -coordinates is given by

$\left\{\begin{array}{rl} A &= L + M + S\\ RG &= L-M+S \\ Y\!B &= L+M-S\end{array}\right.$
What is the appropriate transformation matrix $T\,$ ?

$T={}$

$\matrix{\Box & \Box & \Box \\ \Box & \Box & \Box\\ \Box & \Box & \Box}$

Linear mappings: Matrices and coordinate transformations

Colour and intensity of light: (a)