Let's say $A$ be a Matrix and $\lambda$ be it's Eigen value and the geometric multiplicity of $\lambda$ is strictly less than the Algebraic Multiplicity of the same. As we increase the natural number $k$ in $(A-\lambda I)^k$ the dimension of the null space of the same is increased. And we will get a natural number $m$ such that the dimension of the null space of $(A-\lambda I)^m$ is same as the algebraic multiplicity.
Am I right? If I am right can you please explain me why?