If A and B are invertible matrices,which one | vedclass

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(C) For any invertible matrix $A$,the adjoint formula is $	ext{Adj}(A) = |A|A^{-1}$,so option $A$ is correct.For the determinant of an inverse,$\det(

Vedclass · Accepted Answer

$(A + B)^{-1} = B^{-1} + A^{-1}$

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(C) For any invertible matrix $A$,the adjoint formula is $	ext{Adj}(A) = |A|A^{-1}$,so option $A$ is correct.For the determinant of an inverse,$\det(A^{-1}) = \frac{1}{\det(A)} = (\det(A))^{-1}$,so option $B$ is correct.The property of the inverse of a product is $(AB)^{-1} = B^{-1}A^{-1}$,so option $D$ is correct.However,the inverse of a sum is not equal to the sum of the inverses,i.e.,$(A + B)^{-1} 
eq A^{-1} + B^{-1}$ in general. Thus,option $C$ is incorrect.

If $A$ and $B$ are invertible matrices,which one of the following statements is not correct?

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