If A and B are invertible matrices, which of the following statement is not correct.

Question:

If A and B are invertible matrices, which of the following statement is not correct.

(a) adj $A=|A| A^{-1}$

(b) $\operatorname{det}\left(A^{-1}\right)=(\operatorname{det} A)^{-1}$

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

 

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

Solution:

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

We have, adj $A=|A| A^{-1}, \operatorname{det}\left(A^{-1}\right)=(\operatorname{det} A)^{-1}$ and $(A B)^{-1}=B^{-1} A^{-1}$ all are the properites of inverse of a matrix.

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