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