The function $f: C \to C$ defined by $f(x) =\large\frac{ax+b}{cx+d}$ for $x \in C$ where $bd \neq 0$ reduces to a constant function , if :

Question

$$\begin {array} {1 1} (a)\;a=c & \quad (b)\;b=d \\ (c)\;ab=bc & \quad (d)\;ab=cd \end {array}$$