If`A = [[0 , 1, -1],[4, -3, 4],[3, -3, 4]]` find the transpose of A matrix

Explanation

To find the transpose of the matrix \( A \), we will follow these steps:

1. **Write down the original matrix \( A \)**:
\[ A = \begin{bmatrix} 0 & 1 & -1 \\ 4 & -3 & 4 \\ 3 & -3 & 4 \end{bmatrix} \]

2. **Understand the concept of transpose**:
The transpose of a matrix is obtained by swapping its rows with columns. This means that the first row of the original matrix becomes the first column of the transposed matrix, the second row becomes the second column, and so on.

3. **Transpose the matrix**:
- The first row of \( A \) is \( [0, 1, -1] \), which will become the first column of \( A^T \).
- The second row of \( A \) is \( [4, -3, 4] \), which will become the second column of \( A^T \).
- The third row of \( A \) is \( [3, -3, 4] \), which will become the third column of \( A^T \).

Therefore, the transposed matrix \( A^T \) will be:
\[ A^T = \begin{bmatrix} 0 & 4 & 3 \\ 1 & -3 & -3 \\ -1 & 4 & 4 \end{bmatrix} \]

4. **Final result**:
The transpose of matrix \( A \) is:
\[ A^T = \begin{bmatrix} 0 & 4 & 3 \\ 1 & -3 & -3 \\ -1 & 4 & 4 \end{bmatrix} \]