Question

If $A$ and $B$ are square matrices of order $3,$ then

• A. $\operatorname{adj}(A B)=\operatorname{adj} A+\operatorname{adj} B$
• B. $(A+B)^{-1}=A^{-1}+B^{-1}$
• C. $A B=O \Rightarrow|A|=0$ or $|B|=0$
• D. $A B=O \Rightarrow|A|=0$ and $|B|=0$

Answer 1

Answer: (C)

If $A B=O,$ then either of $A$ and $B$ is necessarily singular.