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KCET2011MathematicsMatrices

If A and B are symmetric matrices of the same order, then which one of the following is not true?

Options

  1. AA+B is symmetric
  2. BA-B is symmetric
  3. CA B+B A is symmetric
  4. DA B-B A is symmetric

Correct answer

D. A B-B A is symmetric

Step-by-step solution

Given, A and B are symmetric matrix of same order. A=A^ , B=B^ (i) (A+B)^ =A^ +B^ =A+B [from Eq. (i)] (A+B) is symmetric. (ii) (A-B)^ - ^ -B^ - -B [from Eq. (i)] (A-B) is symmetric. (iii) aligned (A B+B A)^ &=(A B)^ +(B A)^ &=B^ A^ +A^ B^ &=B A+A B from Eq. (i) ] &=(A B+B A) aligned (A B+B A) is symmetric. (iv) aligned (A B-B A)^ &=(A B)^ -(B A)^ &=B^ A^ -A^ B^ &=B A-A B [from Eq. (i)] &=-(A B-B A) aligned (A B-B A) is skew-symmetric matrix.

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