Question

Let \( A \) and \( B \) be two matrices of suitable orders. Then, which of the following is not correct?

• A. \( (A')' = A \)
• B. \( (kA)' = kA' \), \( k \) is scalar
• C. \( (A' + B')' = A + B \)
• D. \( (AB)' = A'B' \)

Hint:

Transpose of a product follows reverse order: \( (AB)' = B'A' \).

Answer 1

The Correct Option is D

We know that: - Transpose of a transpose: \( (A')' = A \)
- Scalar multiple transposes: \( (kA)' = kA' \)
- Addition under transpose: \( (A' + B')' = A + B \)
- But product: \( (AB)' = B'A' \), not \( A'B' \)
So, Option (D) is incorrect.