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Given that A = αβγα[αβγ-α] and A2 = 3I, then: -

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Question

Given that A = `[(α,β),(γ,-α)]` and A2 = 3I, then:

Options

  • 1 + α2 + βγ = 0

  • 1 − α2 − βγ = 0

  • 3 − α2 − βγ = 0

  • 3 + α2 + βγ = 0

MCQ

Solution

3 − α2 − βγ = 0

Explanation:

A2 = 3I

`[(α^2+βγ,0),(0,βγ+α^2)] = [(3,0),(0,3)]`

3 − α2 − βγ = 0

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