Q. If $A$ and $B$ are symmetric matrices of the same order and $X = AB + BA$ and $Y = AB - BA$, then $(XY)^{T}$ is equal to
A) $XY$
B) $YX$
C) $- YX$
D) None of these
Explanation
(c)
Given that
$X = AB + BA \Rightarrow X = X^{T}$
And
$Y = AB - BA$
$\Rightarrow Y = - Y^{T}$
Now,$(XY)^{T} = Y^{T}X^{T} = - YX$.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.