If A and B are square matrices of size n × n such that A^2 - B^2 = (A - B)(A + B) , then which of the following will be always true? - Mathematics MCQ AIEEE 2006 2026 | ExamTest.live

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If A and B are square matrices of size n \times n such that A^{2} - B^{2} = (A - B) (A + B), then which of the following will be always true?

Solution & Step-by-step Explanation

Expanding the right side: (A - B) (A + B) = A (A + B) - B (A + B) = A^{2} + A B - B A - B^{2} Given: A^{2} - B^{2} = A^{2} + A B - B A - B^{2} Subtracting A^{2} and adding B^{2} to both sides: 0 = A B - B A A B = B A This implies the matrices A and B must commute.

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If A and B are square matrices of size n \times n such that A^{2} - B^{2} = (A - B) (A + B), then which of the following will be always true?

A = B

A B = B A

either of A or B is a zero matrix

either of A or B is an identity matrix

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