Let $M = \left(\begin{array}{ll} a & b \\ c & d \end{array}\right)$ be a matrix of $\mathcal{M}_{2}(\mathbb{C})$. Show that $M$ is similar to a matrix of type $\left(\begin{array}{cc} \alpha & 0 \\ 0 & \beta \end{array}\right)$ or of type $\left(\begin{array}{cc} \alpha & \gamma \\ 0 & \alpha \end{array}\right)$, where $\alpha, \beta$ and $\gamma$ are complex numbers with $\alpha \neq \beta$.