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Let A be a square matrix satisfying (A−2I)(A+I)=O. Then A−1 equals:

1. (A−I)/2
2. (A+I)/2
3. 2(A−I)
4. 2A+I

Correct answer: (A−I)/2

Solution

The equation (A−2I)(A+I)=O implies that A has eigenvalues 2 and -1. The eigenvalue 2 leads to the inverse A−1 being expressed as (A−I)/2, since for eigenvalue 2, the corresponding eigenvector satisfies A*v = 2*v, leading to v = (A−I)/2*v.

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