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Home  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Matrices

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?

$\begin{array}{1 1}(a)\;A=B\\(b)\;AB=BA\\(c)\;Either\;of\;A\;or\;B\;is\;zero\;matrix\\(d)\;Either\;of\;A\;or\;B\;is\;identity\;matrix\end{array}$

1 Answer

$A^2-B^2=(A-B)(A+B)$
$A^2-B^2=A^2+AB-BA-B^2$
$\qquad\;\;\;\;=AB=BA$
Hence (b) is the correct answer.
answered Nov 21, 2013 by sreemathi.v
 

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