Let a, B, a + B be invertible matrices of order n, prove that a ^ - 1 + B ^ - 1 is invertible, and find the inverse of a ^ - 1 + B ^ - 1,

From the reversibility of a and B, we know that a ^ - 1 + B ^ - 1 = a ^ - 1 (a + b) B ^ - 1
It is known that a + B is invertible, so a ^ - 1 + B ^ - 1 is invertible (the product of invertible matrices is still invertible)
And (a ^ - 1 + B ^ - 1) ^ - 1 = [a ^ - 1 (a + b) B ^ - 1] ^ - 1 = B (a + b) ^ - 1A

Let a, B, a + B be invertible matrices of order n, prove that a ^ - 1 + B ^ - 1 is invertible, and find the inverse of a ^ - 1 + B ^ - 1,

Let a, B, a + B be invertible matrices of order n, prove that a ^ - 1 + B ^ - 1 is invertible, and find the inverse of a ^ - 1 + B ^ - 1,

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