If A is a 4 4 matrix of rank 3 and = 0 is an

If A is a 4 × 4 matrix of rank 3 and λ = 0 is an eigenvalue of multiplicity 3, then A is diagonalizable.
In the case of a true statement, explain or prove your answer. In the case of a false statement, give an example to show that the statement is not always true.