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

Answer: (A)

Skew symmetric matrix

Answer 2

The correct option is(A): Skew symmetric matrix.

A and B are symmetric matrices, therefore, we have:
A=A and B=B...(1)

consider
(AB-BA)=(AB)-(BA) [(A-B)=A-B]
=BA-AB[(AB)=BA]
=BA-AB [by(1)]
=-(AB-BA)

Therefore (AB-BA)=-(AB-BA)

Thus,

(AB−BA) is a skew-symmetric matrix.