Chapter 7 - Eigenvalues and Eigenvectors - 7.2 Diagonalization - 7.2 Exercises - Page 360: 24

Cannot guarantee the diagonalization.

We know that for a triangular or diagonal matrix, the eigenvalues are the entries on the diagonal. Hence, here the eigenvalues are: $2,2$. But these are not distinct, so we only have $1$ eigenvalue and the dimensions of the matrix are $2\times2$. Thus, we cannot guarantee the diagonalization.