First you need to find the eigenvalues so you can find the eigen Basis for the matrix (if it exists)

Expanding along the first column we get

So the two eigenvalues are

Using we get the matrix

Reducing we get

This implies that there are two parameters in the solution so let

so the last equation is

so the solution is

So these are the first two eigenvectors

Now using the eigen values we get

Reducing we get

This has 1 parameter in its solution so let

We can see that and

So the solution is

The eigenvectors are the columns of the matrix P.