Markov process intensity matrix

$$X$$ is a Markov process with state space $$(1,2,3)$$. How can I find the matrices of transition probabilities $$P(t)$$ if the generator is $$\begin{bmatrix}-2&2&0\\2&-4&2\\0&2&-2\end{bmatrix}$$?

Can I use Kolmogorov forward equation $$P'(t)=P(t)Q$$ where $$Q$$ is the generator for this problem?