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If A and B are invertible matrices, which of the following statements are correct?

1. adj(A) = |A| * A^(-1)
2. det(A^(-1)) = (det(A))^(-1)
3. (A + B)^(-1) = B^(-1) + A^(-1)

Correct answer: adj(A) = |A| * A^(-1)

Solution

Both options (i) and (ii) are standard matrix identities that always hold for invertible matrices. Option (iii) is false in general: the inverse of a sum does not equal the sum of inverses (unlike scalars).

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