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

Options

  1. A1 only
  2. B2 only
  3. CBoth 1 and 2
  4. DNeither 1 nor 2

Correct answer

B. 2 only

Step-by-step solution

For symmetric matrices, A^ =A, B^ =B(A B-B A)^ =B A-A B=-(A B-B A) (A B-B A) is a skew symmetric matrix (A B-B A) matrix have all diagonal element as zero (statement 1 is incorrect) Sum of all non diagonal elements in (A B-B A)=0 Only 2 is correct.

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