# Should we use all $N$ correspondence points to compute Homography or just $4$ points?

Given correspondences of $$(x,x')$$, we want to find a Homography matrix $$H$$ that maps $$x' = Hx$$. If we use 4 corresponding non - collinear points and the matrix $$H$$ has rank $$n-1$$, then the homogenous equation $$Ah =0$$ has a unique solution up to a constant. Suppose we find more than $$4$$ corresponding pairs of points, we get an overdetermined system of equation and we have to use least squares minimisation to find the solution.

I am curious as to whether it is better to just use $$4$$ points or $$>4$$ points to find the Homography ?

Also, it makes sense that from a linear algebra perspective, I am unable to solve the homogenous equation exactly when we have an overdetermined system. However, from a planar perspective, given my correspondence points are good, shouldn't there be an exact solution ?