QJEEM06Mab2c0: JEE Main 2006 Mathematics - Class 12 JEEM06Mab2c0 Solution: If A and B are square matrices of size n × n such that A 2 − B…

Question

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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?

Accepted Answer

A^{2} - B^{2} = (A - B) (A + B)

A^{2} - B^{2} = A^{2} + A B - B A - B^{2}

\Rightarrow A B = B A

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