Given two matrices \( A = \begin{bmatrix} 2 & 3 \\ 1 & 4 \end{bmatrix} \) and \( B = \begin{bmatrix} 5 & 6 \\ 7 & 8 \end{bmatrix} \), find the product \( AB \).

Step 1 ：Step 1: Let's compute the element at the first row and the first column of \( AB \). The element is the dot product of the first row of \( A \) and the first column of \( B \), which is \( 2*5 + 3*7 = 10 + 21 = 31 \).

Step 2 ：Step 2: Compute the element at the first row and the second column of \( AB \). The element is the dot product of the first row of \( A \) and the second column of \( B \), which is \( 2*6 + 3*8 = 12 + 24 = 36 \).

Step 3 ：Step 3: Compute the element at the second row and the first column of \( AB \). The element is the dot product of the second row of \( A \) and the first column of \( B \), which is \( 1*5 + 4*7 = 5 + 28 = 33 \).

Step 4 ：Step 4: Compute the element at the second row and the second column of \( AB \). The element is the dot product of the second row of \( A \) and the second column of \( B \), which is \( 1*6 + 4*8 = 6 + 32 = 38 \).

Step 5 ：Step 5: The product \( AB \) is then the matrix formed by these four elements: \( \begin{bmatrix} 31 & 36 \\ 33 & 38 \end{bmatrix} \).