Problem

Find the transpose of the matrix \( A = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix} \).

Answer

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Answer

\( A^T = \begin{bmatrix} 1 & 4 & 7 \\ 2 & 5 & 8 \\ 3 & 6 & 9 \end{bmatrix} \).

Steps

Step 1 :The transpose of a matrix is obtained by interchanging its rows into columns or columns into rows. So, the transpose of matrix \( A \), denoted by \( A^T \), is obtained as follows:

Step 2 :\( A^T = \begin{bmatrix} 1 & 4 & 7 \\ 2 & 5 & 8 \\ 3 & 6 & 9 \end{bmatrix} \).

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