Let \( A \) and \( B \) be two matrices of suitable orders. Then, which of the following is not correct?
Show Hint
- \( (A')' = A \)
- \( (kA)' = kA' \), \( k \) is scalar
- \( (A' + B')' = A + B \)
- \( (AB)' = A'B' \)
The Correct Option is D
Solution and Explanation
- 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.
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