1. **State the problem:** We are asked to perform the matrix multiplication of two matrices: $$\begin{bmatrix}-9 & -3 \\ -8 & -2\end{bmatrix} \times \begin{bmatrix}4 & 1 \\ 7 & -3\end{bmatrix}$$ 2. **Check if multiplication is possible:** The first matrix is $2 \times 2$ and the second matrix is $2 \times 2$. Since the number of columns in the first matrix (2) equals the number of rows in the second matrix (2), multiplication is possible. 3. **Recall the formula for matrix multiplication:** If $A$ is $m \times n$ and $B$ is $n \times p$, then the product $AB$ is $m \times p$ with entries: $$ (AB)_{ij} = \sum_{k=1}^n A_{ik} B_{kj} $$ 4. **Calculate each element of the product matrix:** - Element at position (1,1): $$ (-9)(4) + (-3)(7) = -36 - 21 = -57 $$ - Element at position (1,2): $$ (-9)(1) + (-3)(-3) = -9 + 9 = 0 $$ - Element at position (2,1): $$ (-8)(4) + (-2)(7) = -32 - 14 = -46 $$ - Element at position (2,2): $$ (-8)(1) + (-2)(-3) = -8 + 6 = -2 $$ 5. **Write the resulting matrix:** $$\begin{bmatrix}-57 & 0 \\ -46 & -2\end{bmatrix}$$ **Final answer:** $$\boxed{\begin{bmatrix}-57 & 0 \\ -46 & -2\end{bmatrix}}$$