Let a be a square matrix of order n and satisfy a ^ 2-3a + 2E = 0, it is proved that the eigenvalue of a can only be 1 or 2

Let the eigenvalue of a be a, then a ^ 2-3a + 2 is the eigenvalue of a ^ 2-3a + 2E
Given that a ^ 2-3a + 2E = 0, the eigenvalue of zero matrix can only be zero,
So a ^ 2-3a + 2 = 0, that is (a - 1) (a - 2) = 0. So a = 1 or a = 2
That is, the eigenvalue of a can only be 1 or 2

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