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Given matrices:
\[ A = \begin{bmatrix} 1 & 1 \\ -1 & 1 \end{bmatrix}, \quad B = \begin{bmatrix} 0 & 1 \\ -1 & 0 \end{bmatrix} \]

We need to compute \( (A+B) \), \( (A-B) \), \( -(A-B) \), and \( (A+B) \).

### Step 1: Compute \( A+B \)
\[ A+B = \begin{bmatrix} 1+0 & 1+1 \\ -1-1 & 1+0 \end{bmatrix} = \begin{bmatrix} 1 & 2 \\ -2 & 1 \end{bmatrix} \]

### Step 2: Compute \( A-B \)
\[ A-B = \begin{bmatrix} 1-0 & 1-1 \\ -1+1 & 1-0 \end{bmatrix} = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \]

### Step 3: Compute \( -(A-B) \)
\[ -(A-B) = -\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} = \begin{bmatrix} -1 & 0 \\ 0 & -1 \end{bmatrix} \]

### Step 4: Compute \( (A+B) \)
This is repeated from Step 1:
\[ (A+B) = \begin{bmatrix} 1 & 2 \\ -2 & 1 \end{bmatrix} \]

The original request appears to also involve matrix multiplication between these results, so we need to compute:
\[ (A+B) \cdot (A-B) \cdot (-(A-B)) \cdot (A+B) \]

First, calculate \( (A+B) \cdot (A-B) \):
\[ \begin{bmatrix} 1 & 2 \\ -2 & 1 \end{bmatrix} \cdot \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} = \begin{bmatrix} 1 & 2 \\ -2 & 1 \end{bmatrix} \]

Next, calculate \( \begin{bmatrix} 1 & 2 \\ -2 & 1 \end{bmatrix} \cdot \begin{bmatrix} -1 & 0 \\ 0 & -1 \end{bmatrix} \):
\[ \begin{bmatrix} -1 & -2 \\ 2 & -1 \end{bmatrix} \]

Lastly, calculate the final multiplication with \( (A+B) \) again:
\[ \begin{bmatrix} -1 & -2 \\ 2 & -1 \end{bmatrix} \cdot \begin{bmatrix} 1 & 2 \\ -2 & 1 \end{bmatrix} = \begin{bmatrix} (-1)(1) + (-2)(-2) & (-1)(2) + (-2)(1) \\ (2)(1) + (-1)(-2) & (2)(2) + (-1)(1) \end{bmatrix} = \begin{bmatrix} 5 & -4 \\ 4 & 3 \end{bmatrix} \]

The final matrix result for the entire sequence of operations is:
\[ \begin{bmatrix} 5 & -4 \\ 4 & 3 \end{bmatrix} \]

Would you like to delve into any particular step or need help with another question? Here are some related topics you might find interesting:
1. The properties of matrix addition and multiplication.
2. The concept of the identity matrix and its role in matrix operations.
3. How changing the order of matrices in multiplication affects the result.
4. The definition and calculation of the inverse of a matrix.
5. Application of matrix operations in solving systems of linear equations.

**Tip:** Remember that matrix multiplication is not commutative; changing the order can lead to different results.

Jika A = [[1, 1], [-1, 1]] dan B = [[0, 1], [-1, 0]], maka (A+B)(A-B)-(A-B)(A+B) adalah matriks...

Solve the matrix problem involving A+B and A-B, using matrix addition, subtraction, and multiplication. This problem covers advanced matrix operations, including the associative and distributive properties of matrix multiplication.

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