Determine if the statement is true of false, and justify your answer. If A and B are invertible n n matrices, then the inverse of A + B is A 1 + B 1…

If A and B are invertible n × n

 matrices, then the inverse of A + B

 is A−1 + B−1.

True, by the Big Theorem.

True, by the definition of matrix addition.

True, by the definition of invertible matrices.

False. For example, let A = In, and B = In, then A + B = 2In, which is not invertible.

False. For example, let A = In, and B = −In, then A + B = 0n, which is not invertible.