It doesn't matter !
Calculate the determinant of X - lambda I, that is to say the determinant of :
add column c1 to column c2 :
=(1-lambda) [ 1-alpha-lambda-beta ]
lambda is such that the determinant is = 0.
So lambda=1 or lambda=1-(alpha+beta)
These are the eigenvalues Was it clear enough ?
Then calculate the eigenvectors like you've learnt with numbers.