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finding transition matrix given transformed points

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hi, im currently writing a quick program which will figure out the transofmation matrix, given the original points & the transformed output, right now im only concerned with 2D and 2x2 matricies. eg. given these points:
original:
(0, 0)  (0, 1)  ( 1, 1)  ( 1, 0)

transformed:
(0, 0)  (3, 2)  (-1, 4)  (-4, 2)

is this possible? any help would be appreciated.

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with a 2x2 matrix you''ve got 4 unknowns so you need 4 equations.
that means you can get the matrix if you''ve got 2 points

M*p0 = p0''
M*p1 = p1''

if you write this in components you get a system of 4 linear equations with 4 unknowns which is easy to solve.

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