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.