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    How to prove that an orthogonal projection matrix is idempotent

    Homework Statement Prove that [P]^2=[P] (that the matrix is idempotent) Homework Equations The Attempt at a Solution A(A^T*A)^-1 A^T= (A(A^T*A)^-1 A^T)^2 Where A^T is the transpose of A. I have no idea.
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