Find the simple modules of the algebra $A$, where $A = \begin{equation*} \begin{pmatrix} K & 0\\ K & K \end{pmatrix} \end{equation*}$ and $K$ is a field
$\textbf{My attempt:}$
I was thinking about something involving direct sums, I know that $A = E_{1,1}K \oplus E_{2,1}K \oplus E_{2,2}K$, but I don't know how to continue... I guess the summands are the simple modules of $A$. Could you help me?
