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The problem asks to find matrix \( A \) given that:

\[
(AB)^{-1} = \begin{pmatrix} \frac{3}{8} & -\frac{1}{2} \\ -\frac{1}{8} & \frac{1}{2} \end{pmatrix}
\]
and
\[
B^{-1} = \begin{pmatrix} \frac{1}{4} & \frac{1}{8} \\ \frac{1}{4} & -\frac{3}{8} \end{pmatrix}.
\]

### Step-by-step approach:
1. **Inverse of a Product of Matrices:**
   According to matrix properties, we know:
   \[
   (AB)^{-1} = B^{-1} A^{-1}.
   \]
   Therefore, we can express the relationship as:
   \[
   (AB)^{-1} = B^{-1} A^{-1}.
   \]
   This implies:
   \[
   A^{-1} = B (AB)^{-1}.
   \]

2. **Find matrix \( A^{-1} \):**
   We first need the matrix \( B \) to calculate \( A^{-1} \). Using the inverse of matrix \( B^{-1} \), we can find matrix \( B \).

3. **Finding matrix \( B \):**
   We can calculate the inverse of \( B^{-1} \). Let me calculate \( B \) and then use it to find matrix \( A \).The matrix \( A \) is:

\[
A = \begin{pmatrix} 2 & -1 \\ 1 & -1 \end{pmatrix}
\]

Thus, the correct answer is option **b**.

Would you like further clarification or details?

Here are some related questions to expand your understanding:

1. How do you compute the inverse of a matrix?
2. What are the properties of matrix multiplication and their impact on inverses?
3. Why is the order of multiplication important when dealing with matrix inverses?
4. Can all matrices be inverted? If not, why?
5. How do you verify if a matrix is invertible?

**Tip:** When working with matrix inverses, ensure that the matrix is square and has a non-zero determinant, as these are conditions for invertibility.

Jika (AB)^-1 = [ [3/8, -1/2], [-1/8, 1/2] ] dan B^-1 = [ [1/4, 1/8], [1/4, -3/8] ], matriks A = ....

Learn how to find matrix A given the inverses of (AB) and B. This problem involves calculating matrix inversions and using matrix multiplication properties. Ideal for undergraduate linear algebra students.

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