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…

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?
  1. A = B
  2. AB = BA
  3. either of A or B is a zero matrix
  4. either of A or B is an identity matrix

Solution

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

Asked in: JEE Main 2006

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