Question

If A and B are symmetric matrices of the same order, then

• A. AB is a symmetric matrix
• B. A - B is a skew-symmetric matrix
• C. AB + BA is a symmetric matrix
• D. AB - BA is a symmetric matrix

Answer 1

Answer: (C)

AB + BA is a symmetric matrix

Answer 2

$\left(AB + BA\right)^{t} = \left(AB\right)^{t} + \left(BA\right)^{t}$ $= B^{t} A^{t} + A^{t} B^{t} =BA + AB = AB + BA$ $\left(\because A^{t} =A \, \text{and} \, B^{t} =B\right)$