If A and B two squares matrices of order n×n such that A2−B2=(A−B)(A+B) then which of the following will be always true

(A−B)(A+B)=A2+AB−BA−B2=A2−B2 ⇒AB=BA

If A and B two squares matrices of order n×n such that A2−B2=(A−B)(A+B) then which of the following will be always true

(A−B)(A+B)=A2+AB−BA−B2=A2−B2 ⇒AB=BA

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If A and B two squares matrices of order $n \times n$ such that $A^{2} - B^{2} = (A - B) (A + B)$ then which of the following will be always true

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Either A (or) B identity matrix

Either $A (o r) B$ zero matrix

$A B = B A$

$A = B$

answer is B.

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

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If A and B two squares matrices of order n×n such that A2−B2=(A−B)(A+B) then which of the following will be always true

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If A and B two squares matrices of order $n \times n$ such that $A^{2} - B^{2} = (A - B) (A + B)$ then which of the following will be always true