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Let's solve each question one at a time.

### Question 8
Given:
\[
A = \begin{bmatrix} 1 & 0 & 4 \\ 0 & 4 & -2 \end{bmatrix}
\]
and
\[
B = \begin{bmatrix} 6 & -7 & -1 & 8 \end{bmatrix}
\]

we need to find the products \( AB \) and \( BA \).

1. **Calculating \( AB \):**
   Matrix \( A \) has dimensions \( 2 \times 3 \) (2 rows and 3 columns), and matrix \( B \) has dimensions \( 1 \times 4 \) (1 row and 4 columns). To multiply \( AB \), matrix \( B \) would need to be transposed to match dimensions, or alternatively, the multiplication might be invalid if dimensions are incompatible as shown.

2. **Calculating \( BA \):**
   We also need

Given A = [[1, 0, 4], [0, 4, -2]] and B = [6, -7, -1, 8], find AB and BA. If the answer is a 1x1 matrix, just enter it as a number. Otherwise, enter it as a matrix. Use the matrix multiplication to find element 2,3 of the product in Question 9.

Learn how to perform matrix multiplication with given matrices A and B, find AB and BA, and determine specific elements in the product matrix. This problem explores fundamental concepts of matrix algebra, suitable for advanced high school or undergraduate students.

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