Question

Is the sum of two invertible matrices necessarily invertible?

Answer 1

No

Explanation:

A minimal example with `1xx1` matrices would be:

`(1) + (-1) = (0)`

A less trivial example with `2xx2` matrices would be:

`((1, 1), (0, 1)) + ((-1, 1), (0, -1)) = ((0, 2), (0, 0))`