Let A and B be symmetric matrices of the same order. Which of the following statements is/are correct? I. (AB-BA) is also a symmetric matrix. II. (BA-AB) is a skew-symmetric matrix. Select the answer using the code given below.

NDA 2026 Mathematics question

Let and be symmetric matrices of the same order. Which of the following statements is/are correct? I. is also a symmetric matrix. II. is a skew-symmetric matrix. 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

Since and : (AB-BA)^T = B^TA^T-A^TB^T = BA-AB = -(AB-BA). So is skew-symmetric, not symmetric in general, and

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Question ID VK-030392