1. The problem is to understand and work with matrices. 2. A matrix is a rectangular array of numbers arranged in rows and columns. 3. Important rules include matrix addition, multiplication, and finding the determinant. 4. For example, if we have two matrices $A = \begin{bmatrix}1 & 2 \\ 3 & 4\end{bmatrix}$ and $B = \begin{bmatrix}5 & 6 \\ 7 & 8\end{bmatrix}$, their sum is $A + B = \begin{bmatrix}1+5 & 2+6 \\ 3+7 & 4+8\end{bmatrix} = \begin{bmatrix}6 & 8 \\ 10 & 12\end{bmatrix}$. 5. Matrix multiplication is done by taking the dot product of rows and columns. For $A \times B$, the element in the first row and first column is $1\times5 + 2\times7 = 5 + 14 = 19$. 6. The determinant of a 2x2 matrix $\begin{bmatrix}a & b \\ c & d\end{bmatrix}$ is $ad - bc$. 7. For matrix $A$, determinant is $1\times4 - 2\times3 = 4 - 6 = -2$. This is a basic introduction to matrices with examples of addition, multiplication, and determinant calculation.