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The problem provided is in Estonian, and I will first translate it to make sure the question is clear.

**Translation:**
1. Let \( A \) be a matrix of order 4, and its determinant is given as \( |A| = -2 \).
2. Let matrix \( B \) be the inverse of matrix \( A \), and matrix \( C \) be the opposite (negative) of matrix \( A \).
3. Find the following determinants:
   - \( |C| \)
   - \( |AB| \)
   - \( |A + C| \)
   - \( |CB| \)

Now, let's proceed with solving these step by step:

### 1. \( |C| \)
Matrix \( C \) is the opposite of matrix \( A \), so:
\[
C = -A
\]
For determinants, we know that:
\[
|C| = |-A| = (-1)^n \cdot |A|
\]
Where \( n \) is the order of the matrix. Since \( A \) is a 4x4 matrix (\( n = 4 \)):
\[
|C| = (-1)^4 \cdot |A| = 1 \cdot (-2) = -2
\]
Thus, \( |C| = -2 \).

### 2. \( |AB| \)
Matrix \( B \) is the inverse of matrix \( A \), so:
\[
AB = I \quad \text{(the identity matrix)}
\]
The determinant of the identity matrix is always 1, regardless of the size:
\[
|AB| = |I| = 1
\]

### 3. \( |A + C| \)
Since \( C = -A \), we have:
\[
A + C = A - A = 0 \quad \text{(the zero matrix)}
\]
The determinant of the zero matrix is 0:
\[
|A + C| = 0
\]

### 4. \( |CB| \)
Matrix \( C = -A \), so:
\[
CB = (-A)B = -(AB)
\]
We already know that \( AB = I \), so:
\[
CB = -I
\]
The determinant of \( -I \) is \( (-1)^n \cdot |I| \). Since \( n = 4 \):
\[
|CB| = (-1)^4 \cdot |I| = 1 \cdot 1 = 1
\]

### Final answers:
- \( |C| = -2 \)
- \( |AB| = 1 \)
- \( |A + C| = 0 \)
- \( |CB| = 1 \)

Do you have any questions or want further details on any step?

Here are five related questions to expand on the topic:
1. What properties of determinants are used to calculate \( |C| \) from \( A \)?
2. How does the determinant of the identity matrix always remain 1?
3. Why is the determinant of a sum involving opposites of matrices zero?
4. How would the results change if \( A \) were a 3x3 matrix instead?
5. Can a zero matrix ever have a non-zero determinant?

**Tip:** The determinant of a matrix's inverse is always the reciprocal of the original matrix's determinant.

Let A be a matrix of order 4, with |A| = -2. Let B be the inverse of A and C be the opposite matrix of A. Find the following determinants: |C|, |AB|, |A + C|, |CB|.

Solve a problem involving matrix determinants for matrices A, B, and C, including the determinant of an inverse matrix and properties of matrix addition. The solution involves key linear algebra concepts such as the properties of determinants and inverse matrices.

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