1. The problem is to multiply two 3x3 matrices: Matrix A = \( \begin{bmatrix}8 & 2 & 5 \\ 1 & 2 & 2 \\ 0 & 4 & 3 \end{bmatrix} \) and Matrix B = \( \begin{bmatrix}1 & 6 & 2 \\ 7 & 3 & 2 \\ 2 & 4 & 9 \end{bmatrix} \). 2. To find the product matrix C = A \times B, each element \( c_{ij} \) is computed by the dot product of the i-th row from A and j-th column from B: \[ c_{ij} = \sum_{k=1}^3 a_{ik} b_{kj} \] 3. Calculate each element: - \( c_{11} = 8 \times 1 + 2 \times 7 + 5 \times 2 = 8 + 14 + 10 = 32 \) - \( c_{12} = 8 \times 6 + 2 \times 3 + 5 \times 4 = 48 + 6 + 20 = 74 \) - \( c_{13} = 8 \times 2 + 2 \times 2 + 5 \times 9 = 16 + 4 + 45 = 65 \) - \( c_{21} = 1 \times 1 + 2 \times 7 + 2 \times 2 = 1 + 14 + 4 = 19 \) - \( c_{22} = 1 \times 6 + 2 \times 3 + 2 \times 4 = 6 + 6 + 8 = 20 \) - \( c_{23} = 1 \times 2 + 2 \times 2 + 2 \times 9 = 2 + 4 + 18 = 24 \) - \( c_{31} = 0 \times 1 + 4 \times 7 + 3 \times 2 = 0 + 28 + 6 = 34 \) - \( c_{32} = 0 \times 6 + 4 \times 3 + 3 \times 4 = 0 + 12 + 12 = 24 \) - \( c_{33} = 0 \times 2 + 4 \times 2 + 3 \times 9 = 0 + 8 + 27 = 35 \) 4. Write the product matrix C: $$ C = \begin{bmatrix} 32 & 74 & 65 \\ 19 & 20 & 24 \\ 34 & 24 & 35 \end{bmatrix} $$ Final answer: The product of the two matrices is \( \begin{bmatrix}32 & 74 & 65 \\ 19 & 20 & 24 \\ 34 & 24 & 35 \end{bmatrix} \).