Math Help - det(A+B) ?? det(A) + det(B)

1. det(A+B) ?? det(A) + det(B)

I'm thinking
det(A+B) >= det(A) + det(B)

but I need a proof on this to formally prove something else.

2. Re: det(A+B) ?? det(A) + det(B)

Originally Posted by rubix
I'm thinking
det(A+B) >= det(A) + det(B)

but I need a proof on this to formally prove something else.

If $A=\left(\begin{array}{cc}1&0\\0&1\end{array}\right )$ and $B=\left(\begin{array}{cc}-1&0\\0&-1\end{array}\right)$ then $A+B = O$ so $det(A+B)= 0$

but $det(A) +det(B) = 1+1=2$.

3. Re: det(A+B) ?? det(A) + det(B)

Originally Posted by rubix
I'm thinking
det(A+B) >= det(A) + det(B)

but I need a proof on this to formally prove something else.
As zoek has shown, your lemma is not true. What is the "something else" you're trying to prove?