If A and B are two square matrices such that B = -A^-1 B A, then (A + B)^2 is :
- A. 0
- B. A^2 + 2AB + B^2
- C. A + B
- D. A^2 + B^2
Answer: D. A^2 + B^2
Explanation: From B = -A^-1 B A, multiplying by A from left gives AB = -BA, so AB + BA = 0. Thus (A + B)² = A² + AB + BA + B² = A² + B².