If beginbmatrix lalpha - betall Igamma -lalpha lend bmatrix is the square root of second order unit matrix-

The correct option is B α^2+βγ 1=0 [ α amp; β; γ amp; α ][ α amp; β; γ amp; α ]=[ 1 amp; 0; 0 amp; 1 ] ⇒[ α^2+βγ ...

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Byju's Answer

Standard IX

Mathematics

Multiplication of Matrices

If beginbmatr...

Question

$I f [\begin{matrix} α & β γ & - α \end{matrix}] is the square root of second order unit matrix, T h e n α, β a n d γ should satisfy the relation$

$1 - α^{2} + β γ = 0$

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$α^{2} + β γ - 1 = 0$

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$1 + α^{2} + β γ = 0$

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$1 - α^{2} - β γ = 0$

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Solution

The correct option is B
$α^{2} + β γ - 1 = 0$

$[\begin{matrix} α & β γ & - α \end{matrix}] [\begin{matrix} α & β γ & - α \end{matrix}] = [\begin{matrix} 1 & 0 0 & 1 \end{matrix}] \Rightarrow [\begin{matrix} α^{2} + β γ & 0 0 & α^{2} + β γ \end{matrix}] = [\begin{matrix} 1 & 0 0 & 1 \end{matrix}] \Rightarrow α^{2} + β γ - 1 = 0$

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If[αβγ−α]is the square root of second order unit matrix, Then α,β and γ should satisfy the relation

The correct option is B α2+βγ−1=0 [αβγ−α][αβγ−α]=[1001]⇒[α2+βγ00α2+βγ]=[1001]⇒α2+βγ−1=0

$I f [\begin{matrix} α & β γ & - α \end{matrix}] is the square root of second order unit matrix, T h e n α, β a n d γ should satisfy the relation$