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If A and B are square matrices of size n × n such that A² − B² = (A − B)(A + B), then which of the following will be always true?

1. A = B
2. AB = BA
3. either of A or B is a zero matrix
4. either of A or B is identity matrix

Correct answer: AB = BA

Solution

The equation A² − B² = (A − B)(A + B) holds true for any square matrices A and B, indicating that the matrices commute (AB = BA) under this condition, which is a fundamental property of matrix multiplication.

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