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Math Help - Eigenvalue Proof

  1. #1
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    Eigenvalue Proof

    Suppose that A is an n x n matrix with the property that A^2=A.
    a) I have to show that if lambda is an eigenvalue of A, then lambda= 1 or 0.
    b) Also I have to prove that A is diagonalizable.

    I'm not sure how the property helps me find the eigenvalues of the matrix A.
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  2. #2
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    If Ax = \lambda x then A^2x = A(Ax) = A(\lambda x) = \lambda^2x. So if A^2 = A and x\ne0 it follows that \lambda^2 = \lambda.
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