How to find multiplicity of eigenvalues?

Question

So i have this matrix:

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Sorry for the formatting, I'm new here and any help would be great.

We compute the characteristic polynomial

$p(\lambda)= {\rm det}(A − \lambda I d)= (\lambda + 2)^2 (1 − λ)$

So from here I know that one of the root is 1 and the other one is -2. However, it states on the answer sheet that the multiplicity of -2 is 2 ? How come ? I don't see two -2 roots in the equation .

Somebody please help?

Answer 1

Think of your characteristic equation as:

$$p(\lambda) = (\lambda + 2)(\lambda + 2)(1 - \lambda)$$

to see the multiplicity of eigenvalues better.