Let A and B be symmetric matrices of same order, then which one of the following is correct regarding (AB-BA)? 1. Its diagonal entries are equal but nonzero 2. The sum of its non-diagonal entries is zero Select the correct answer using the code given below :

NDA 2023 Mathematics question

Let and be symmetric matrices of same order, then which one of the following is correct regarding ? 1. Its diagonal entries are equal but nonzero 2. The sum of its non-diagonal entries is zero Select the correct answer using the code given below :

(A)1 only
(B)2 onlyCorrect
(C)Both 1 and 2
(D)Neither 1 nor 2

Answer: (B)

Solution

(AB-BA)^T = B^TA^T-A^TB^T = BA-AB = -(AB-BA), so is skew-symmetric. In a skew-symmetric matrix every diagonal entry is zero, so statement 1 (equal

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Question ID VK-029537