If \( A = \begin{bmatrix} 1 & 3 \end{bmatrix} \) and \( B = \begin{bmatrix} 2 \\ 4 \end{bmatrix} \), what is the product of \( A \) and \( B \)?

Step 1 ：Step 1: Determine the dimensions of the matrices. \( A \) is a 1x2 matrix and \( B \) is a 2x1 matrix. Since the number of columns in \( A \) is equal to the number of rows in \( B \), the matrices can be multiplied.

Step 2 ：Step 2: Multiply the elements of the first row of \( A \) by the corresponding elements of the first column of \( B \), and then add the products. This will give the element in the first row and first column of the product matrix. \( (1*2) + (3*4) = 2 + 12 = 14 \)

Step 3 ：Step 3: Continue this process for all rows of \( A \) and all columns of \( B \). Since \( A \) only has one row and \( B \) only has one column, the product matrix only has one element.