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Question
Choose the correct alternative.
If A and B are square matrices of order n × n such that A2 – B2 = (A – B)(A + B), then which of the following will be always true?
Options
AB = BA
either of A or B is a zero matrix
either of A and B is an identity matrix
A = B
Solution
A2 – B2 = (A – B)(A + B)
∴ A2 – B2 = A2 + AB – BA – B2
∴ 0 = AB – BA
∴ AB = BA.
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