I have the following question :
$A$ is a $n \times n$ matrix, and this is the characteristic polynom $$p(x)=(x+3)^2(x-1)(x-5)$$
Then I can conclude that $n=4$ since the number of the roots is $4$, now this is my question :
Can I conclude for any $\lambda \neq -3,1,5$ that $\lambda I-A$ and $A- \lambda I$ are invertible matrixs?
I think this statement is true, but I'd like to be sure of that, since this is critical point.