Question

If the order of the matrix \( A \) is \( 3 \times 2 \), then the order of matrix \( A^T \) is:

Hint:

The order of the transpose of a matrix is obtained by switching its rows and columns.

Answer 1

Step 1: Understanding matrix transposition.
The order of the transpose of a matrix \( A \) is obtained by swapping the number of rows and columns of \( A \). If \( A \) is of order \( m \times n \), then \( A^T \) (the transpose of \( A \)) will be of order \( n \times m \). Step 2: Applying this to the given matrix.
Since the order of matrix \( A \) is \( 3 \times 2 \), the order of \( A^T \) will be \( 2 \times 3 \). Step 3: Conclusion.
Thus, the order of matrix \( A^T \) is \( 2 \times 3 \).