Let T(z) = (az+b)/(cz+d), where ad-bc≠0, be any linear fractional transformation other than T(z) = z. Show that T^-1 = T only if d = -a.
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First we have to find the inverse. To do so we must solve the above equation in z.
(cz+d)T=(az+b) ---> czT+dT=az+b ---> czT-az=b-dT ---> z=(b-dT)/(cT-a)
At this point if we let z be T^(-1) and T be z in the above ...
Linear fractional transformations and implicit form are investigated and discussed.