Question

If matrices \( A \) and \( B \) are of order \( 1 \times 3 \) and \( 3 \times 1 \) respectively, then the order of \( A'B' \) is:

• A. \( 1 \times 1 \)
• B. \( 3 \times 1 \)
• C. \( 1 \times 3 \)
• D. \( 3 \times 3 \)

Hint:

The order of the product of matrices depends on the number of rows of the first matrix and the number of columns of the second matrix.

Answer 1

The Correct Option is D

Step 1: Analyze the dimensions of the transposed matrices. - Given \( A \) of order \( 1 \times 3 \), its transpose \( A' \) has order \( 3 \times 1 \). - Given \( B \) of order \( 3 \times 1 \), its transpose \( B' \) has order \( 1 \times 3 \). Step 2: Find the order of the product. The order of \( A'B' \) is given by multiplying the number of rows of \( A' \) and the number of columns of \( B' \): \[ (3 \times 1) \times (1 \times 3) = 3 \times 3 \] Final Answer: \[ \boxed{3 \times 3} \]