1. The problem is to understand and work with matrices, which are rectangular arrays of numbers arranged in rows and columns. 2. A matrix is usually denoted by a capital letter, for example, $A$, and its elements are written as $a_{ij}$ where $i$ is the row number and $j$ is the column number. 3. Important operations with matrices include addition, subtraction, and multiplication. 4. For addition and subtraction, matrices must be of the same size, and you add or subtract corresponding elements. 5. For multiplication, the number of columns in the first matrix must equal the number of rows in the second matrix. 6. The product matrix $C = AB$ has elements calculated by $$c_{ij} = \sum_{k=1}^n a_{ik} b_{kj}$$ where $n$ is the number of columns in $A$ (or rows in $B$). 7. Example: If $A = \begin{bmatrix}1 & 2 \\ 3 & 4\end{bmatrix}$ and $B = \begin{bmatrix}5 & 6 \\ 7 & 8\end{bmatrix}$, then $$C = AB = \begin{bmatrix}1\times5 + 2\times7 & 1\times6 + 2\times8 \\ 3\times5 + 4\times7 & 3\times6 + 4\times8\end{bmatrix} = \begin{bmatrix}19 & 22 \\ 43 & 50\end{bmatrix}$$ 8. This shows how to multiply two matrices step-by-step. 9. Understanding these basics allows you to perform more complex matrix operations and applications in algebra and other fields.