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Let A and B be square matrices satisfying B = -A⁻¹BA. Then what is the value of (A + B)²?

1. O
2. A² + B²
3. A² + 2AB + B²
4. A + B

Correct answer: A² + B²

Solution

The equation B = -A⁻¹BA implies a specific relationship between A and B that leads to the cancellation of the cross term when expanding (A + B)², resulting in A² + B².

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