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Home  >>  CBSE XII  >>  Math  >>  Matrices

If A is square matrix such that $A^2=A,$show that $(I+A)^3=7A+I.$

1 Answer

LHS:-
 
$(I+A)^3$
 
$\Rightarrow (I+A)^2.(I+A)$
 
$\Rightarrow (I^2+A^2+2IA).(I+A)$
 
$(I^2+A+2IA).(I+A)$ [By replacing $A^2$ by A]
 
$(I+A+2A).(I+A)$
 
$(I+3A).(I+A)$
 
$I^2+3AI+AI+3A^2$ [Relace $A^2$=A]
 
$I^2+4AI+3A.$
 
$\Rightarrow I+4A+3A$
 
$\Rightarrow I+7A\Rightarrow RHS.$

 

answered Mar 8, 2013 by sreemathi.v
 

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