Determine whether the given matrices are inverses of each other by computing their product.
\[
A=\left[\begin{array}{rr}
4 & 2 \\
3 & -1
\end{array}\right], B=\left[\begin{array}{rr}
-1 & 2 \\
3 & -2
\end{array}\right]
\]
Select the correct choice below and fill in the answer box to complete your choice.
(Type an integer or simplified fraction for each matrix element.)
A. The given matrices are not inverses of each other because their product is the matrix
B. The given matrices are inverses of each other because their product is the matrix

Step 1 ：Given two matrices A and B as follows:

Step 2 ：\[A=\left[\begin{array}{rr} 4 & 2 \\ 3 & -1 \end{array}\right], B=\left[\begin{array}{rr} -1 & 2 \\ 3 & -2 \end{array}\right]\]

Step 3 ：To determine if these two matrices are inverses of each other, we need to multiply them together. If the product is the identity matrix, then the two matrices are inverses of each other. The identity matrix is a square matrix with ones on the main diagonal and zeros elsewhere. For a 2x2 matrix, the identity matrix is:

Step 4 ：\[I=\left[\begin{array}{rr} 1 & 0 \\ 0 & 1 \end{array}\right]\]

Step 5 ：So, we compute the product of matrices A and B:

Step 6 ：\[A \times B = \left[\begin{array}{rr} 2 & 4 \\ -6 & 8 \end{array}\right]\]

Step 7 ：The product of matrices A and B is not the identity matrix. Therefore, matrices A and B are not inverses of each other.

Step 8 ：\[\boxed{\text{The given matrices are not inverses of each other because their product is the matrix } \left[\begin{array}{rr} 2 & 4 \\ -6 & 8 \end{array}\right]}\]