Q.

If for the matrix A=1-ααβ,AAT=I2 then the value of α4+β4 is:

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a

2

b

1

c

4

d

3

answer is B.

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Detailed Solution

Given  A=1-ααβAAT=I1−ααβ1α−αβ=10011+α2α−αβα−αβα2+β2=1001 Hence, 1+α2=1⇒α=0 and α2+β2=1 ⇒β2=1  Therefore, α4+β4=1
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