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?

A 2 − B 2 = ( A − B ) ( A + B ) A 2 − B 2 = A 2 + A B − B A − B 2 ⇒ A B = B A

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Mathematics - Matrices Question with Solution | TestHub

MathematicsMatricesGeneralEasy2 minPYQ_2006

MathematicsEasysingle choice

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?

Options:

Answer:

Solution:

$A^{2} - B^{2} = (A - B) (A + B)$ $A^{2} - B^{2} = A^{2} + A B - B A - B^{2}$ $\Rightarrow A B = B A$

Stream:JEESubject:MathematicsTopic:MatricesSubtopic:General

⏱ 2mℹ️ Source: PYQ_2006

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