Prove that the inverse of the bilinear transformation of

Question

Question: Prove that the inverse of the bilinear transformation of Problem is itself a bilinear transformation.

Problem: The transformation

Z = (az + b)/(cz + d), ad - bc ≠ 0,

Is called a bilinear transformation. Show that this transformation is conformal for

z ≠ -d/c

And has the property that circles in the z-plane are transformed into circles in the Z-plane (allowing a straight line to be regarded as a circle through the point at infinity).