Under what conditions the function y = (ax+b)/(cx+d),(ad - bc) not equals to 0 is it’s own inverse?

y = b - dx/ cx - a
It should be equal to original function
b - dx/ cx - a = ax + b/cx + d
bcx + bd - dcx^2 - d^2x = acx^2 + bcx - a^2x - ab

By this, we get a = -d should be the other condition.
Thanks
Bharat
askiitians faculty
IIT Delhi