Ex 3.3, 11 - If A, B are symmetric matrices, then AB - BA - Ex 3.3

  1. Chapter 3 Class 12 Matrices
  2. Serial order wise
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Ex 3.3, 11 If A, B are symmetric matrices of same order, then AB − BA is a A. Skew symmetric matrix B. Symmetric matrix C. Zero matrix D. Identity matrix A and B are symmetric matrices, ∴ A’ = A and B’ = B Consider (AB – BA)’ = (AB)’ – (BA)’ = B’A’ – A’B’ = BA − AB = − (AB – BA) ∴ (AB – BA)’ = − (AB – BA) Thus, (AB − BA) is a skew-symmetric matrix. ∴ Correct answer is A.

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