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Show that the Matrix a is Unitary Where a = [ α + I γ − β + L β + L α − I γ ] is Unitary If α 2 + β 2 + γ 2 + ∂ 2 = 1 - Applied Mathematics 1

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Show that the matrix A is unitary where A = `[[alpha+igamma,-beta+idel],[beta+idel,alpha-igamma]]` is unitary if `alpha^2+beta^2+gamma^2+del^2=1` 

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Solution

Given, A is Unitary 

Consider, 

Similarlly, 

Substituting (2),(3),(4)&(5) in (1), 

Comparing corresponding terms, we get, 

unitary if `alpha^2+beta^2+gamma^2+del^2=1` 

 

Concept: Inverse of a Matrix
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