Question

Say true or false:

If A & B are symmetric matrices of same order then $AB-BA$ is symmetric.

• A. True
• B. False

Answer 1

The correct option is B False

Since $A$ and $B$ are symmetric, therefore $A^{\prime }=A$ and $B^{\prime }=B$
Thus
${(AB-BA)}^{\prime }={\left(AB\right)}^{\prime }-{\left(BA\right)}^{\prime }=B^{\prime }{A}^{\prime }-A^{\prime }{B}^{\prime }=BA-AB=-(AB-BA)$
$\Rightarrow AB-BA$ is skew-symmetric matrix.