Problem
Given the following matrix, \[A = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix}\], find the transpose of matrix A.
Solution
Step 1 ：The transpose of a matrix is found by interchanging its rows into columns. So, the transpose of matrix A, denoted by \(A^T\), is given as follows:
Step 2 ：\[A^T = \begin{bmatrix} 1 & 4 & 7 \\ 2 & 5 & 8 \\ 3 & 6 & 9 \end{bmatrix}\]
