If M^T is the transpose of a 2 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 :

NDA 2026 Mathematics question

If is the transpose of a matrix M, then which of the following is/are correct? I. if M is symmetric. II. if M is anti-symmetric. Select the answer using the code given below :

(A)I only
(B)II onlyCorrect
(C)Both I and II
(D)Neither I nor II

Answer: (B)

Solution

Statement I: if is symmetric, , so , whereas . These are equal only when $|M| =

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Question ID VK-030272