Consider the matrix A=(210021002)A = \begin{pmatrix} 2 & 1 & 0 \\ 0 & 2 & 1 \\ 0 & 0 & 2 \end{pmatrix}A=200120012 Which statement about diagonalizability is TRUE?
AAA is diagonalizable because it has three linearly independent eigenvectors
AAA is NOT diagonalizable because the geometric multiplicity of eigenvalue 2 is less than its algebraic multiplicity
AAA is diagonalizable because it is upper triangular with real entries
AAA is diagonalizable because all its eigenvalues equal 2