Answer to Question #236792 in Algebra for moe

Question

Let A and B be n×n matrices such that $\textup{det}(A)\neq 0$ and $\textup{det}(B)\neq 0$. Consider the following statements. Based on the properties of determinants which of the following is false? 

1. $\textup{det}(AB)=\textup{det}(BA)$
2. If $A=−B then \textup{det}(A)=(-1)^{n}\textup{det}(B)$
3. $\textup{det}(A^{T}B^{T})=\textup{det}(AB)$
4. $\textup{det}((AB)^{-1})=\frac{1}{\textup{det}(A)\textup{det}(B)}$
5. $\textup{det}(AB)=\textup{det}(A)+\textup{det}(B)$

Answer 1

Option 5 is false becuase $det(AB)=det(A).det(B)$