# Sum of invertible matrices is invertible?

1. Oct 5, 2008

### soul5

1. The problem statement, all variables and given/known data

Is the sum of two invertible matrices necessarily invertible?

3. The attempt at a solution

I don't know plz help.

2. Oct 5, 2008

Try a couple of small examples - use $$2 \times 2$$
One small hint: both $$2$$ and $$-2$$ are invertible real numbers, but their sum isn't invertible.