If A=begin{bmatrix} a_{11} & a_{12} & a_{13} | vedclass

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(B) Given matrices are $A = \begin{bmatrix} a_{11} & a_{12} & a_{13} \ a_{21} & a_{22} & a_{23} \end{bmatrix}$ and $B = \begin{bmatrix} b_{11} & b_{1

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The orders of $A^T B^T A$ and $B^T A A^T B$ are equal

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(B) Given matrices are $A = \begin{bmatrix} a_{11} & a_{12} & a_{13} \ a_{21} & a_{22} & a_{23} \end{bmatrix}$ and $B = \begin{bmatrix} b_{11} & b_{12} & b_{13} \ b_{21} & b_{22} & b_{23} \end{bmatrix}$.Both matrices $A$ and $B$ have order $2 	imes 3$.Therefore,the order of $A^T$ and $B^T$ is $3 	imes 2$.Now,let us check the order of the matrices in option $B$:The order of $A^T B^T A$ is $(3 	imes 2) 	imes (3 	imes 2) 	imes (2 	imes 3)$,which is not defined because the inner dimensions do not match.However,checking the order of $A^T B B^T A$:Order of $A^T B B^T A = (3 	imes 2) 	imes (2 	imes 3) 	imes (3 	imes 2) 	imes (2 	imes 3) = 3 	imes 3$.Order of $B^T A A^T B = (3 	imes 2) 	imes (2 	imes 3) 	imes (3 	imes 2) 	imes (2 	imes 3) = 3 	imes 3$.Since both expressions $A^T B B^T A$ and $B^T A A^T B$ result in a $3 	imes 3$ matrix,their orders are equal.

If $A=\begin{bmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \end{bmatrix}$ and $B=\begin{bmatrix} b_{11} & b_{12} & b_{13} \\ b_{21} & b_{22} & b_{23} \end{bmatrix}$,then which one of the following is true?

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