Sum of invertible matrices is invertible?

[soul5]

Homework Statement

Is the sum of two invertible matrices necessarily invertible?

The Attempt at a Solution

I don't know please help.

 

[statdad]

Try a couple of small examples - use $$2 \times 2$$
matrices that you know are invertible.

One small hint: both $$2$$ and $$-2$$ are invertible real numbers, but their sum isn't invertible.