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Given two matrices A and B satisfying AB = B and BA = A, what is the value of A² + B²?
- 2AB
- 2BA
- A + B
- AB
Correct answer: 2AB
Solution
The value of A² + B² equals 2AB due to the given conditions AB = B and BA = A, which allows for the simplification of A² + B² into 2AB by substituting the given equalities into the expression.
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