Given $\det(A+B) = 0$ or $\det(AB) = 0$, what can be said for $\det(A)$ and $\det(B)$? 
Given $\det(A+B) = 0$, what can be said for $\det(A)$ and $\det(B)$?

I was thinking that one is maybe the inverse of the other? Im honestly so confused and new at this :c 

Given $\det(AB) = 0$, what can you say for $\det(A)$ and $\det(B)$?

for the second part I wrote that if $A$ and $B$ are square matrices then one of them has $\det$ $0$, if they are not the $\det$ is undefined. is that right? thanks in advance 
 A: You can say nothing for the first question.


*

*Both can be invertibile if say $A=I$ and $B=-I$.

*No one is invertibile if say $A=0=B$.

*One is and second is not invertibile if say $A = I$ and $B= \pmatrix{-1&0\\0&0}$.



For the second, since we have $\det(AB)= \det(A)\det(B)$ then clearly one is not invertibile.
A: The answer to the second is correct. The determinant is only defined for square matrices, and $\det(AB) = \det(A)\det(B)$, so if $\det(AB)=0,$ one of $\det(A)$ or $\det(B)$ is $0$. 
As for sums, in general, you can't say anything about $\det(A)$ or $\det(B)$ given knowledge of $\det(A+B)$. Take for example
$$
A = \left[\begin{array}{cccc}
2 &  0&0&0 \\
0&1&0&0\\
0&0&1&0\\
0&0&0&1
\end{array}\right] \qquad \textrm{and} \qquad 
B=\left[\begin{array}{cccc}
0&0&0&2\\
0&0&1&0\\
0&1&0&0\\
1&0&0&0
\end{array}\right]
$$
Both have a determinant of $2$, but $\det(A+B)=0$. This will in fact be the case no matter what the top left entry of $A$ or the top right entry of $B$ is. 
A: 1) If it is given det(A+B)=0 it is not necessary that det(A)=0 or det(B)=0 independently.
2) If det(AB)=0 Either det(A)=0 or det(B)=0 as rules of Matrices clearly state det(AB)=det(A)*det(B)
