If A and B are non-singular matrices and oper | vedclass

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(C) We know that for any non-singular matrix $M$,$M^{-1} = \frac{\operatorname{Adj}(M)}{\operatorname{det}(M)}$,which implies $\operatorname{Adj}(M) =

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$\operatorname{Adj}(AB)$

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(C) We know that for any non-singular matrix $M$,$M^{-1} = \frac{\operatorname{Adj}(M)}{\operatorname{det}(M)}$,which implies $\operatorname{Adj}(M) = \operatorname{det}(M) \cdot M^{-1}$.Given the expression $((\operatorname{det} A)(\operatorname{det} B)) B^{-1} A^{-1}$.Since $\operatorname{det}(AB) = \operatorname{det}(A) \cdot \operatorname{det}(B)$,we can write the expression as $\operatorname{det}(AB) \cdot (B^{-1} A^{-1})$.Using the property of matrix inversion,$(AB)^{-1} = B^{-1} A^{-1}$.Therefore,the expression becomes $\operatorname{det}(AB) \cdot (AB)^{-1}$.By the definition of the adjoint matrix,this is equal to $\operatorname{Adj}(AB)$.

If $A$ and $B$ are non-singular matrices and $\operatorname{det}(AB)=(\operatorname{det} A)(\operatorname{det} B)$,then $((\operatorname{det} A)(\operatorname{det} B)) B^{-1} A^{-1} =$

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