1. **State the problem:** We are given two matrices $A = \begin{bmatrix} 5 & -1 \\ 0 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 3 \\ 4 & -2 \end{bmatrix}$ and need to find their sum $A + B$. 2. **Formula for matrix addition:** To add two matrices of the same size, add their corresponding elements: $$ (A + B)_{ij} = A_{ij} + B_{ij} $$ 3. **Apply the formula element-wise:** $$ A + B = \begin{bmatrix} 5+1 & -1+3 \\ 0+4 & 2+(-2) \end{bmatrix} $$ 4. **Calculate each element:** $$ = \begin{bmatrix} 6 & 2 \\ 4 & 0 \end{bmatrix} $$ 5. **Final answer:** The sum of matrices $A$ and $B$ is $$ \boxed{\begin{bmatrix} 6 & 2 \\ 4 & 0 \end{bmatrix}} $$