Affine mapping/Fixed points/Identity/Exercise

Let ${}E$ be an affine space of dimension ${}n$, and let

$\psi \colon E\longrightarrow E$

denote an affine mapping. Let ${}P_{1},\ldots ,P_{n+1}\in E$ be affinely independent points, and suppose that they are also fixed points of ${}\psi$. Show that ${}\psi$ is the identity.

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