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Let
A
=
[
1
0
0
0
α
β
0
β
α
]
A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & \alpha & \beta \\ 0 & \beta & \alpha \end{bmatrix}
A
=
1
0
0
0
α
β
0
β
α
…
Mathematics
Problem
Let
A
=
[
1
0
0
0
α
β
0
β
α
]
A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & \alpha & \beta \\ 0 & \beta & \alpha \end{bmatrix}
A
=
1
0
0
0
α
β
0
β
α
and
∣
2
A
∣
3
=
2
21
|2A|^3 = 2^{21}
∣2
A
∣
3
=
2
21
where
α
,
β
∈
Z
\alpha, \beta \in Z
α
,
β
∈
Z
, Then a value of
α
\alpha
α
is (A) 9 (B) 17 (C) 3 (D) 5
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