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If $A$ and $B$ are two matrices such that $AB=B$ and $BA=A$ then $A^2+B^2=$
$\begin{array}{1 1}(A)\;2AB&(B)\;2BA\\(C)\;A+B&(D)\;AB\end{array}$
jeemain
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matrices
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asked
Apr 23, 2014
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sreemathi.v
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Aug 22, 2014
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1 Answer
Given :
$AB=B$
$BA=A$
$A^2+B^2=AA+BB$
$\Rightarrow A(BA)+B(AB)$
$\Rightarrow (AB)A+(BA)B$
$\Rightarrow BA+AB$
$\Rightarrow A+B$
Hence (C) is the correct answer.
answered
Apr 23, 2014
by
sreemathi.v
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