Solve the matrix equation $AX = 2X + B$ where $$A = \begin{bmatrix} 3 & 0 & 0 \cr 0 & 1 & -1 \cr 0 & 1 & 4 \end{bmatrix} \quad\text{ and }\quad B = \begin{bmatrix} 1 & 2\cr -1 & 1 \cr 0 & -3 \end{bmatrix}$$
I understand that it should be like $$X = (A - 2E)^{-1} B$$ but what is the inverse of $-2E$?
Hint
Let $A_{m\times m}$ and $B_{n\times n}$ be two square and invertible matrices; therefore$$\begin{bmatrix}A_{m\times m}&0_{m\times n}\\0_{n\times m}&B_{n\times n}\end{bmatrix}^{-1}=\begin{bmatrix}A^{-1}_{m\times m}&0_{m\times n}\\0_{n\times m}&B^{-1}_{n\times n}\end{bmatrix}$$