# Uniqueness of homography

Let $(z_{1},z_{2},z_{3})$ and $(z'_{1},z'_{2},z'_{3})$ be two $3$-tuples of complex coordinates of non collinear points. How can I prove that there exists a unique homography $h$ such that $h(z_{i})=z'_{i}$ for $i \in \left \{ 1,2,3 \right \}$ ? Thank you

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Sorry for that but I changed my question now since I wanted to delete it because I had found the answer but couldn't know how to do so. –  user20010 Jan 11 '12 at 9:10
I clicked on it but all what appeared is a "vote to delete the post" even if it is my own post ! –  user20010 Jan 11 '12 at 10:03