1. **State the problem:** We are asked to perform the matrix multiplication of two 2x2 matrices: $$\begin{bmatrix} 5 & 6 \\ -9 & -1 \end{bmatrix} \times \begin{bmatrix} -1 & -8 \\ -6 & 2 \end{bmatrix}$$ 2. **Recall the formula for matrix multiplication:** For two matrices $A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}$ and $B = \begin{bmatrix} e & f \\ g & h \end{bmatrix}$, the product $AB$ is: $$AB = \begin{bmatrix} ae + bg & af + bh \\ ce + dg & cf + dh \end{bmatrix}$$ 3. **Check if multiplication is possible:** Both matrices are 2x2, so multiplication is possible. 4. **Calculate each element of the product matrix:** - Top-left element: $$5 \times (-1) + 6 \times (-6) = -5 + (-36) = -41$$ - Top-right element: $$5 \times (-8) + 6 \times 2 = -40 + 12 = -28$$ - Bottom-left element: $$-9 \times (-1) + (-1) \times (-6) = 9 + 6 = 15$$ - Bottom-right element: $$-9 \times (-8) + (-1) \times 2 = 72 - 2 = 70$$ 5. **Write the resulting matrix:** $$\begin{bmatrix} -41 & -28 \\ 15 & 70 \end{bmatrix}$$ **Final answer:** $$\boxed{\begin{bmatrix} -41 & -28 \\ 15 & 70 \end{bmatrix}}$$