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?

(a) A = B 

(b) AB = BA

(c) either A or B is a zero matrix

(d) either A or B is an identity matrix.

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1 Answers

(b) : Give A2 – B2 = (A + B)(A – B)
=> 0 = BA – AB
=> BA = AB

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