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Maths-

General

Easy

Question

If A = $open square brackets table row 0 1 row cell negative 1 end cell 0 end table close square brackets$ and (aI₂ + bA)² = A, then -

a = b = $\sqrt{2}$
a = b = 1/ $\sqrt{2}$
a = b = $\sqrt{3}$
a = b = 1/ $\sqrt{3}$

The correct answer is: a = b = 1/ $square root of 2$

we are given that A = $open square brackets table row 0 1 row cell negative 1 end cell 0 end table close square brackets$ and (aI2 + bA)2 = A, then we need to find the correct option
$left parenthesis a I plus b A right parenthesis squared space space equals left parenthesis a I plus b A right parenthesis left parenthesis a I plus b A right parenthesis space equals a squared I squared space plus a b I A plus b a A I plus b squared A squared space space space equals a squared I plus 2 a b A plus b squared space A squared space space left parenthesis because I space squared equals I comma I A equals A I right parenthesis space equals a squared I plus 2 a b A minus b squared space I left parenthesis because A space space 2 space space equals negative I right parenthesis space equals left parenthesis a squared minus b squared space right parenthesis I plus 2 a b A space E q u a t i n g space c o r r e s p o n d i n g space e l e m e n t s space i n space left parenthesis a I plus b A right parenthesis squared space space a n d space A squared space comma space w e space g e t space a squared minus b squared space space equals 0 space a n d space 2 a b equals 1 space s o l v i n g space t h i s space w e space g e t space a equals b equals plus-or-minus space fraction numerator 1 over denominator root index blank of 2 end fraction$

Therefore the correct option is choice 2

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