Given the matrices \( A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{bmatrix} \) and \( B = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix} \), find the product of \( AB \).

Step 1 ：\( AB = \begin{bmatrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{bmatrix} \times \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix} \)

Step 2 ：To find \( AB \), we perform the dot product of the rows of \( A \) with the columns of \( B \). This gives us a new matrix \( C \) with dimensions 3x3

Step 3 ：For the first element \( c_{11} \) of matrix \( C \), we calculate \( c_{11} = a_{11} \times b_{11} + a_{12} \times b_{21} = 1 \times 1 + 2 \times 4 = 9 \)

Step 4 ：We repeat this process for each element of the resulting matrix \( C \)

Step 5 ：\( AB = \begin{bmatrix} 9 & 12 & 15 \\ 19 & 26 & 33 \\ 29 & 40 & 51 \end{bmatrix} \)