Is the invertibility of (a + b) matrix equal to the invertibility of a + if not, what

Generally, it does not hold, but when a, B, a + B are orthogonal matrices, there is (a + b) ^ - 1 = a ^ - 1 + B ^ - 1
If a, B, a ^ - 1 + B ^ - 1 are all reversible, then a + B is reversible, and its inverse is a ^ - 1 (a ^ - 1 + B ^ - 1) ^ - 1B ^ - 1

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