Question

Which of the following statements is false:

• A. If $|A|=0$, then $\operatorname{ladj} A \mid=0$
• B. Adjoint of a diagonal matrix of order $3 \times 3$ is a diagonal matrix
• C. Product of two upper triangular matrices is a upper triangular matrix
• D. $\operatorname{adj}(A B)=\operatorname{adj}(A) \operatorname{adj}(B)$

Answer 1

Answer: (D)

We have
$ \operatorname{adj}(A B)=\operatorname{adj}(B) \operatorname{adj}(A)$
$\text { and not } \operatorname{adj}(A B)=\operatorname{adj}(A) \operatorname{adj}(B)$