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### Question 1:
You are asked to find the determinant of matrix \( A \), which is given as:

\[
A = \begin{pmatrix} 2 & -2 \\ 1 & 5 \end{pmatrix}
\]

The determinant of a 2x2 matrix is calculated using the formula:

\[
\text{det}(A) = (a \times d) - (b \times c)
\]

For matrix \( A \):

\[
a = 2, \, b = -2, \, c = 1, \, d = 5
\]

\[
\text{det}(A) = (2 \times 5) - (-2 \times 1) = 10 + 2 = 12
\]

So, the determinant of \( A \) is **12**. The correct answer is **c)**.

---

### Question 2:
For the second question, you are given the matrix \( A \):

\[
A = \begin{pmatrix} e & f \\ g & h \end{pmatrix}
\]

The determinant of this 2x2 matrix is also calculated as:

\[
\text{det}(A) = (e \times h) - (f \times g)
\]

This matches the formula given as option **a)**, so the correct answer is **a)**.

---

### Question 3:
You are given two matrices \( A \) and \( B \) and asked to find the sum of their determinants:

\[
A = \begin{pmatrix} -2 & 7 \\ -2 & 3 \end{pmatrix}, \quad B = \begin{pmatrix} 4 & 5 \\ 1 & -3 \end{pmatrix}
\]

#### Step 1: Determinant of \( A \)

Using the formula for a 2x2 determinant:

\[
\text{det}(A) = (-2 \times 3) - (7 \times -2) = -6 + 14 = 8
\]

#### Step 2: Determinant of \( B \)

\[
\text{det}(B) = (4 \times -3) - (5 \times 1) = -12 - 5 = -17
\]

#### Step 3: Sum of Determinants

\[
\text{det}(A) + \text{det}(B) = 8 + (-17) = -9
\]

Thus, the correct answer is **d)**.

---

Would you like further details or have any questions?

Here are some related questions to explore further:
1. How do we compute the determinant of a 3x3 matrix?
2. What is the significance of a matrix having a zero determinant?
3. Can you explain how the determinant is used in solving systems of equations?
4. How do properties of determinants change if we scale or transpose a matrix?
5. What is the geometric interpretation of a matrix determinant?

**Tip:** The determinant is crucial in determining if a matrix is invertible. If the determinant is zero, the matrix does not have an inverse.

1. Determinan dari matriks A adalah ...
A = [[2, -2], [1, 5]]
a) 8  b) 9  c) 12  d) 10

2. Jika A = [[e, f], [g, h]], maka det A = ...
a) eh - fg  b) eh + fg  c) eh = fg  d) fg + eh

3. Jika A = [[-2, 7], [-2, 3]] dan B = [[4, 5], [1, -3]], maka det(A) + det(B) = ...
a) -37  b) 9  c) 37  d) -9

Learn how to calculate the determinant of a 2x2 matrix with practice problems and solutions. Problems include finding determinants for matrices A and B and using the determinant formula. Suitable for students in Grades 10-12 studying linear algebra.

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