1. Tardigrade
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  3. Mathematics
  4. If A and B are square matrices of size n × n such that A2-B2=(A-B)(A+B), Then which of the following will be always true?

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Q. 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?

Solution:

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