1. **State the problem:** Multiply the two given 2x2 matrices: $$\begin{bmatrix}-9 & -3 \\ -8 & -2\end{bmatrix} \times \begin{bmatrix}4 & 1 \\ 7 & -3\end{bmatrix}$$ 2. **Recall the formula for matrix multiplication:** If $$A = \begin{bmatrix}a & b \\ c & d\end{bmatrix}$$ and $$B = \begin{bmatrix}e & f \\ g & h\end{bmatrix}$$, then $$AB = \begin{bmatrix}ae + bg & af + bh \\ ce + dg & cf + dh\end{bmatrix}$$ 3. **Calculate each element of the product matrix:** - Top-left element: $$(-9)(4) + (-3)(7) = -36 - 21 = -57$$ - Top-right element: $$(-9)(1) + (-3)(-3) = -9 + 9 = 0$$ - Bottom-left element: $$(-8)(4) + (-2)(7) = -32 - 14 = -46$$ - Bottom-right element: $$(-8)(1) + (-2)(-3) = -8 + 6 = -2$$ 4. **Write the resulting matrix:** $$\begin{bmatrix}-57 & 0 \\ -46 & -2\end{bmatrix}$$ 5. **Conclusion:** The operation is possible and the product matrix is as above.