1. Eigenvalues

Hi everyone, I am needing some help. I have the matrix

A= [2 1/2]
.....[-1/2 1]

According to my book, the eigenvalue for this is λ1= λ2=3/2 and the eigenvector is
v=[1]
...[-1]

However, this is not what I am getting. I'm not seeing where they are getting the 3/2 from. I know the process of finding the eigenvalue because I have successfully solved my other homework problems but this one is stumping me. Can someone show how to get the 3/2 eigenvalue?

2. by $\det(A-\lambda I)=0$

$\lambda^2-3\lambda+ \frac{9}{4}=0$
$\left(\lambda-\frac{3}{2}\right)^2=0$
gives $\lambda = \frac{3}{2}$