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Let A and B be any two 3 × 3 matrices. If A is symmetric and B is skew symmetric, then the matrix A B - B A is

Options

  1. Askew symmetric
  2. BI or -   I , where I is an identity matrix
  3. Csymmetric
  4. Dneither symmetric nor skew symmetric

Correct answer

C. symmetric

Step-by-step solution

A square matrix P is said to be a symmetric matrix, if P T = P and it is said to be a skew symmetric matrix, if P T = - P . Given A T = A ,   B T = - B Now, A B - B A T = A B T - B A T = B T A T - A T B T = ( - B ) A - A ( - B ) = A B - B A ⇒ A B - B A is a symmetric matrix.

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