SOLUTION: If the matrices A and B are two invertible matrices, then (A + B) is also invertible is this statement true or false and why?

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Question 1006562: If the matrices A and B are two invertible matrices, then (A + B) is also invertible

is this statement true or false and why?
Answer by ikleyn(52785) About Me  (Show Source):
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False.

For a given invertible matrix  A  take the matrix  B  as  B = -A.

Then  B  is invertible,  and A + B = 0  (zero matrix),  which is not invertible.