Let `A= [[a,b,c],[b,c,a],[c,a,b]]` then find tranpose of A matrix

Explanation

To find the transpose of the matrix \( A \), we follow the definition of the transpose, which states that the rows of the original matrix become the columns of the transposed matrix.

Given the matrix:
\[ A = \begin{bmatrix} a & b & c \\ b & c & a \\ c & a & b \end{bmatrix} \]

### Step 1: Identify the rows of matrix \( A \)
The rows of matrix \( A \) are:
1. Row 1: \( [a, b, c] \)
2. Row 2: \( [b, c, a] \)
3. Row 3: \( [c, a, b] \)

### Step 2: Create the transpose by converting rows to columns
Now, we will convert each row into a column for the transposed matrix \( A^T \):
- The first row \( [a, b, c] \) becomes the first column.
- The second row \( [b, c, a] \) becomes the second column.
- The third row \( [c, a, b] \) becomes the third column.

Thus, the transposed matrix \( A^T \) is:
\[ A^T = \begin{bmatrix} a & b & c \\ b & c & a \\ c & a & b \end{bmatrix} \]

### Final Result
The transpose of matrix \( A \) is:
\[ A^T = \begin{bmatrix} a & b & c \\ b & c & a \\ c & a & b \end{bmatrix} \]