Show that the matrix is diagonalizable and find a diagonal matrix similar to the given matrix.
actually you don't need the matrix P. You will find that the char poly has a repeated eigenvalue of
You will need to show that gives two eigen vectors.
After you have shown this the similar matrix will be the matrix with the eigenvalues of the char. poly down the diagonal.
What I am saying is this
If you make your matrix P such that
like this this
Where the first column is the vector corrisponding to the eigenvalue 2 then the diagonal matrix will look like this
If you move exchange the first two columns P would look like this
Then D would look like this
Both of the above are similar to the original matrix.
I hope this clears it up.