arrow_back Let $A$ and $B$ be $n \times n$ matrices. Which of the following is true?

Question

Let $A$ and $B$ be $n \times n$ matrices. Which of the following is true?

 

A) $\operatorname{det}(A)=\operatorname{det}(-A)$

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

C) $\operatorname{det}(A+B)=\operatorname{det}(A)+\operatorname{det}(B)$

D) $\operatorname{det}(A \cdot B)=\operatorname{det}(A) \cdot \operatorname{det}(B)$

E) none of the above