If A and B are invertible matrices then which of the following statement is NOT correct?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $(A+B)^{-1}=A^{-1} + B^{-1}$
The statements involving invertible matrices are checked below.
$\text{adj}\,A = |A|A^{-1}$ is always true for any invertible matrix.
$|A^{-1}| = |A|^{-1}$ is also always true.
$(AB)^{-1} = B^{-1}A^{-1}$ is the correct inverse rule.
$(A+B)^{-1} = A^{-1} + B^{-1}$ is not true in general for matrices, so this statement is incorrect.
Final answer: the incorrect statement is $(A+B)^{-1}=A^{-1}+B^{-1}$