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

If a square matrices $A$ and $B$ are such that $AA^{\theta}=A^{\theta}A$, $BB^{\theta}=B^{\theta}B$, $AB^{\theta}=B^{\theta}A$ then $AB(AB)^{\theta}$ is equal to

$\begin{array}{1 1}(a)\;B^{\theta}A^{\theta}AB&(b)\;BA^{\theta}AB\\(c)\;BA^{\theta}A^{\theta}B&(d)\;None\;of\;these\end{array}$

1 Answer

Given :
$AB^{\theta}=B^{\theta}A$
So that
$(AB^{\theta})^{\theta}=(B^{\theta}A)^{\theta}$
$\Rightarrow (B^{\theta})^{\theta}A^{\theta}=A^{\theta}B$
Now
$AB(AB)^{\theta}=AB.B^{\theta}A^{\theta}$
$\Rightarrow AB^{\theta}BA^{\theta}$
$\Rightarrow B^{\theta}AA^{\theta}B$
$\Rightarrow B^{\theta}A^{\theta}AB=(AB)^{\theta}AB$
Hence (a) is correct answer.
answered Nov 26, 2013 by sreemathi.v
 
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