Multiply the following matrices: \( A = \begin{bmatrix} 3 & 4 \\ 2 & 1 \\ 5 & 6 \end{bmatrix} \) and \( B = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix} \)

Step 1 ：The product of two matrices is found by multiplying the elements of the first row of the first matrix by the elements of the first column of the second matrix and summing the products. Then, the process is continued with the remaining rows and columns. Using this method, the first element of the product matrix, located at the first row and first column, is given by \(3*1 + 4*4 = 19\).

Step 2 ：Continuing this process, the remaining elements of the product matrix are found to be: \(3*2+4*5 = 26\), \(3*3+4*6 = 33\), \(2*1+1*4 = 6\), \(2*2+1*5 = 9\), \(2*3+1*6 = 12\), \(5*1+6*4 = 29\), \(5*2+6*5 = 40\), and \(5*3+6*6 = 51\).

Step 3 ：Therefore, the product matrix is \( \begin{bmatrix} 19 & 26 & 33 \\ 6 & 9 & 12 \\ 29 & 40 & 51 \end{bmatrix} \)