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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 \(\begin{bmatrix} -3 & 1 \\ -4 & 6 \end{bmatrix}\)."

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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).

Determine whether the given matrices are inverses of each other by computing their product. A = [[5, 1], [2, -1]], B = [[-1, 1], [2, -4]]

Learn how to determine whether the given matrices A = [[5, 1], [2, -1]] and B = [[-1, 1], [2, -4]] are inverses by computing their matrix product. This problem covers the concept of matrix multiplication and the conditions for inverse matrices. Suitable for Grades 10-12 students.

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