Let $A$ be a matrix that is defined like this:
$$A_{ij}=\begin{cases} \alpha, & \text{if i=j} \\ \beta , & \text{if i $\ne$ j} \end{cases} $$ So I realized this matrix looks somehow like this $$ \begin{pmatrix} \alpha & \beta & \beta \\ \beta & \alpha & \beta \\ \beta & \beta & \alpha \\ \end{pmatrix} $$
I tried to manipulate the rows to get an upper triangular matrix but couldn't succeed, am I in the right direction... some help?:)