we really don't need the condition what we need for our matrix to be diagonalizable is let the eigenvalues of are thus:

then find the eigenvectors corresponding to each eigenvalue and put them in a matrix so that the first column is the eigenvector corresponding to the first eigenvalue on i.e. and the

second and the third columns are the eigenvectors corresponding to and respectively. the result would be this matrix: this matrix satisfies

the matrix that you're looking for is just the inverse of you'll get: [note that the entries of all matrices are in ]