First slide

Transpose of matrix

Question

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

Moderate

A

$X Y$
B

$Y X$
C

$- Y X$
D

None of these

Solution

Given that X = AB + BA
$\begin{array}{ll} \Rightarrow X = X^{T} and Y = AB - BA \\ \Rightarrow Y = - Y^{T} \\ Now (XY)^{T} = Y^{T} X^{T} = - YX \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App