Find, if possible, a nonsingular matrix P such that is diagonal.
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.