Question

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

Answer 1

Matrices A and B are defined as symmetric matrices with same order, therefore,

A ′ =A and B ′ =B.

Then,

( AB−BA ) ′ = ( AB ) ′ − ( BA ) ′ = B ′ A ′ − A ′ B ′ =BA−AB =−( AB−BA )

It is observed that ( AB−BA ) ′ =−( AB−BA ).

Thus, ( AB−BA ) is a skew-symmetric matrix.

Therefore, the correct option is (A).