If A and B are invertible matrices of same order, then which one of the following is NOT true?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $adj\, (AB) = (adj\, A) (adj\, B)$
Check each identity.
(A) $(AB)^{-1}=B^{-1}A^{-1}$ is always true.
(B) $\text{adj}(AB)=\text{adj}(A)\text{adj}(B)$ is false because the correct identity is $\text{adj}(AB)=\text{adj}(B)\text{adj}(A)$.
(C) $\text{adj}(A^{T})=(\text{adj}A)^{T}$ is true.
(D) $|A^{-1}|=(|A|)^{-1}$ is true.
Final answer: $\text{adj}(AB)=(\text{adj}A)(\text{adj}B)$ is NOT true