1. Stating the problem. Subtract the following matrices and compute $A - B$. $$A = \begin{pmatrix}5 & -2 & 0\\3 & 4 & -1\end{pmatrix}, \quad B = \begin{pmatrix}1 & 0 & 2\\-1 & 5 & 3\end{pmatrix}$$ 2. Formula and rules. Matrix subtraction is performed elementwise. If $A$ and $B$ are the same size then $C = A - B$ where $c_{ij} = a_{ij} - b_{ij}$. Make sure matrices have the same dimensions before subtracting. 3. Intermediate work: compute each entry. Compute $c_{11} = 5 - 1 = 4$. Compute $c_{12} = -2 - 0 = -2$. Compute $c_{13} = 0 - 2 = -2$. Compute $c_{21} = 3 - (-1) = 4$. Compute $c_{22} = 4 - 5 = -1$. Compute $c_{23} = -1 - 3 = -4$. 4. Assemble the result. Therefore $$A - B = \begin{pmatrix}4 & -2 & -2\\4 & -1 & -4\end{pmatrix}$$. 5. Explanation. This result is found by subtracting corresponding entries of $A$ and $B$ one by one. You can check each entry to verify the subtraction.