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Question

Choose the correct answer in the following question:
If A=[αβγα]
is such that A2=I. then
(a)1+α2+βγ=0(b)1α2+βγ=0(c)1α2βγ=0(d)1+α2βγ=0


Solution

Given, A2=I
AA=I[αβγα][αβγα]=[1001][α2+βγαβαβαγγαγβ+α2]=[1001]
On comparing the corresponding elements, we have
α2+βγ=1α2+βγ1=01α2βγ=1
Hence, (c)is the correct option.


Mathematics

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