If \( M^T \) is the transpose of a \( 2 \times 2 \) matrix M, then which of the following is/are correct ? I. \( |M + M^T| = |M| + |M^T| \) if M is symmetric. II. \( |M + M^T| = 0 \) if M is anti-symmetric. Select the answer using the code given below :
- A. I only
- B. II only ✓
- C. Both I and II
- D. Neither I nor II
Correct Answer: B. II only
Explanation
If M is symmetric, M = M^T, then |M+M^T| = |2M| = 4|M|, but |M| + |M^T| = 2|M|, so I is false. If M is anti-symmetric, M^T = -M, so M+M^T = 0, giving determinant 0. Thus II is correct.
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