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Question: Answered & Verified by Expert
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?
MathematicsMatricesJEE MainJEE Main 2006
Options:
  • A
    A = B
  • B
    AB = BA
  • C
    either of A or B is a zero matrix
  • D
    either of A or B is an identity matrix
Solution:
2275 Upvotes Verified Answer
The correct answer is:
AB = BA
$A^2-B^2=(A-B)(A+B)$
$A^2-B^2=A^2+A B-B A-B^2$
$\Rightarrow A B=B A$

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