Exams › GATE › Engineering Mathematics

The statements P and Q are related to matrices A and B, which are conformable for both addition and multiplication. P: \((A + B)^T = A^T + B^T\) Q: \((AB)^T = A^T B^T\) Which one of the following options is CORRECT?

1. P is TRUE and Q is FALSE
2. Both P and Q are TRUE
3. P is FALSE and Q is TRUE
4. Both P and Q are FALSE

Correct answer: P is TRUE and Q is FALSE

Solution

The transpose distributes over addition, so \((A+B)^T = A^T + B^T\) is true. For products, the correct identity is \((AB)^T = B^T A^T\), not \(A^T B^T\), so Q is false.

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