diagonalization , help me to to find out which one

Question

Could anyone only help me to find out which one is diagonalizable?

Answer 1

Hint: It's not hard to see that \begin{align} v_1= \begin{bmatrix} 1\\ 1 \\ 0\\ 0 \end{bmatrix}, \ \ v_2= \begin{bmatrix} 1\\ -1 \\ 0\\ 0 \end{bmatrix} \end{align} are eigenvectors with corresponding eigenvalues, $3$ and $1$ respectively. Consider $B-3I$ and $B-I$ and see what you get.