The product of the given matrices $A$ and $B$ is:

$A \times B = \begin{bmatrix} -3 & 1 \\ -4 & 6 \end{bmatrix}$

Since this product is not the identity matrix, $A$ and $B$ are not inverses of each other. The correct answer is option B: "The given matrices are not inverses of each other because their product is the matrix $\begin{bmatrix} -3 & 1 \\ -4 & 6 \end{bmatrix}$."

Do you want more details or have any questions about this solution?

Here are five related questions for further understanding:

1. What is the identity matrix, and how is it used to verify matrix inverses?
2. How can you calculate the inverse of a matrix?
3. What are the properties of matrix multiplication?
4. Can non-square matrices have inverses?
5. What happens if you reverse the order of multiplication in this case?

Tip: When multiplying matrices, the order matters—$A \times B \neq B \times A$ in general (this is called non-commutative property of matrix multiplication).