Given that the matrix A of order n satisfies a ^ 2-2a-3e = 0, it is proved that the eigenvalue of a can only be - 1 or 3. How to prove that it can only be - 1? (- e-A) (3e-a) = 0, but how can we prove that it can only be - 1 or 3?

Given that the matrix A of order n satisfies a ^ 2-2a-3e = 0, it is proved that the eigenvalue of a can only be - 1 or 3. How to prove that it can only be - 1? (- e-A) (3e-a) = 0, but how can we prove that it can only be - 1 or 3?

Just go to the determinant on both sides of the equation and get two equations, that is - e-A = 0 or 3e-a = 0
Then according to the characteristic polynomial of the matrix λ e-A = 0, we can see that the eigenvalue of a is - 1 or 3

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