A T BA T -A- A T B T A TB- A T B T AC- AA T B TD- B T A T A

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Byju's Answer

Standard XII

Mathematics

Transpose of a Matrix

A T BA T =A. ...

Question

$(A^{T} B A)^{T}$ =

A^{T} B^{T} A^{T}

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A^{T} B^{T} A

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A A^{T} B^{T}

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B^{T} A^{T} A

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Solution

The correct option is B $A^{T} B^{T} A$
The main principle that has to be applied is, $(X Y)^{T} = Y^{T} X^{T}$
Using this in our present case,
$(A^{T} B A)^{T} = (B A)^{T} . (A^{T})^{T}$
$= A^{T} B^{T} A$

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(ATBA)T =

The correct option is B ATBTAThe main principle that has to be applied is, (XY)T=YTXT Using this in our present case, (ATBA)T=(BA)T.(AT)T =ATBTA

$(A^{T} B A)^{T}$ =

The correct option is B $A^{T} B^{T} A$
The main principle that has to be applied is, $(X Y)^{T} = Y^{T} X^{T}$
Using this in our present case,
$(A^{T} B A)^{T} = (B A)^{T} . (A^{T})^{T}$
$= A^{T} B^{T} A$