I have a question:
Let $A=\begin{bmatrix} \mathbb K & 0\\ \mathbb K & \mathbb K \end{bmatrix}$. I need to find all of its simple modules and their projective covers.
I know that the simple modules of $A$ are in equivalence with the simple modules of $\frac{A}{Rad(A)}=\begin{bmatrix} \mathbb K & 0\\ 0 & \mathbb K \end{bmatrix}$. Which means that they are simple modules of $\mathbb K^2$ and are identified with the 2 copies of $\mathbb K$.
But I do not know how to find their projective covers?
Can someone let me know what are those and how can we establish them?
Many thanks!