If $A$ and $B$ are symmetric matrices of the same order and $X = A B + B A$ and $Y = A B - B A$ , then ${X Y}^{T}$ is equal to

X Y

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Y X

No worries! We‘ve got your back. Try BYJU‘S free classes today!

- Y X

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

none of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $- Y X$
Given A and B are symmetric.
$A^{T} = A, B^{T} = B$
Consider ${X Y}^{T} = (A B + B A) (A B - B A)^{T}$
$= (A B + B A) ((A B)^{T} - (B A)^{T})$
$= (A B + B A) (B^{T} A^{T} - A^{T} B^{T})$
$= (A B + B A) (B A - A B)$
$= - (A B - B A) (A B + B A)$
$= - Y X$
$\Rightarrow X Y^{T} = - Y X$

Suggest Corrections

Similar questions

(X Y)^{T}

If A and B are symmetric matrices of the same order and X = AB + BA and Y = AB - BA, then $(X Y)^{T}$ is equal to

A

B

X = A B + B A

Y = A B - B A,

(X Y)^{T}

If A and B are symmetric matrices of the same order and X = AB + BA and Y = AB - BA, then $(X Y)^{T}$ is equal to

A

B

X = A B + B A

Y = A B - B A,

(X Y)^{T}

Join BYJU'S Learning Program