If A and B are non-singular matrices of the s | vedclass

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(B) We know that for any square matrix $M$,$M \cdot 	ext{adj}(M) = |M|I$,where $I$ is the identity matrix.For the product matrix $AB$,we have $(AB) \

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$(Adj. B)(Adj. A)$

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(B) We know that for any square matrix $M$,$M \cdot 	ext{adj}(M) = |M|I$,where $I$ is the identity matrix.For the product matrix $AB$,we have $(AB) \cdot 	ext{adj}(AB) = |AB|I = |A||B|I$.Now,consider the expression $(Adj. B)(Adj. A)$:$(AB) \cdot (Adj. B \cdot Adj. A) = A(B \cdot Adj. B) \cdot Adj. A$$= A(|B|I) \cdot Adj. A$$= |B|(A \cdot Adj. A)$$= |B|(|A|I)$$= |A||B|I = |AB|I$.Since $(AB) \cdot 	ext{adj}(AB) = |AB|I$ and $(AB) \cdot (Adj. B \cdot Adj. A) = |AB|I$,and $A, B$ are non-singular (so $AB$ is invertible),we can multiply by $(AB)^{-1}$ on the left to get:$	ext{adj}(AB) = 	ext{adj}(B) \cdot 	ext{adj}(A)$.

If $A$ and $B$ are non-singular matrices of the same order,then $\text{Adj}(AB)$ is:

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