If A and B are square matrices of size n × n such that {A^2} - {B^2} = left( {A - B} right)left( {A

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3 and 4 .Determinants and Matrices

easy

If $A$ and $B$ are square matrices of size $n \times n$ such that ${A^2} - {B^2} = \left( {A - B} \right)\left( {A + B} \right)$ ,then which ofthe following will be always true ?

A

$A=B$

B

$AB=BA$

C

either of $A$ or $B$ is a zero matrix

D

either of $A$ or $B$ is identity matrix

(AIEEE-2006)

Solution

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

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

$\Rightarrow A B=B A$

Standard 12

Mathematics

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