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AP EAMCET2009MathematicsMatrices

Let A and B be two symmetric matrices of same order. Then, the matrix A B-B A is

Options

  1. Aa symmetric matrix
  2. Ba skew-symmetric matrix
  3. Ca null matrix
  4. Dthe identity matrix

Correct answer

B. a skew-symmetric matrix

Step-by-step solution

Given, A=A^ , B=B^ Now, (A B-B A)^ =(A B)^ -(B A)^ aligned & =B^ A^ -A^ B^ & =B A-A B & =-(A B-B A) aligned A B-B A is a skew-symmetric matrix.

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