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(C) The order of matrix $A$ is $3 	imes 3$ and the order of matrix $B$ is $2 	imes 3$.For matrix addition $A+B$,the orders must be identical,which i

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$A'B'$

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(C) The order of matrix $A$ is $3 	imes 3$ and the order of matrix $B$ is $2 	imes 3$.For matrix addition $A+B$,the orders must be identical,which is not the case here.For matrix multiplication $AB$,the number of columns in $A$ $(3)$ must equal the number of rows in $B$ $(2)$,which is not true.Now,consider the transpose matrices:$A'$ is of order $3 	imes 3$.$B'$ is of order $3 	imes 2$.For the product $A'B'$,the number of columns in $A'$ $(3)$ equals the number of rows in $B'$ $(3)$. Thus,$A'B'$ is defined.For the product $B'A'$,the number of columns in $B'$ $(2)$ must equal the number of rows in $A'$ $(3)$,which is not true.Therefore,the correct option is $C$.

If $A = \begin{bmatrix} 1 & 2 & 3 \\ 5 & 0 & 7 \\ 6 & 2 & 5 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 3 & 5 \\ 0 & 0 & 2 \end{bmatrix}$,then which of the following is defined?

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