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Mathematics
Mathematics
Problem
Let
A
A
A
be a
2
×
2
2 \times 2
2
×
2
matrix with real entries such that
A
′
=
α
A
+
I
A' = \alpha A + I
A
′
=
α
A
+
I
, where
α
∈
R
−
{
−
1
,
1
}
\alpha \in \mathbb{R} - \{-1, 1\}
α
∈
R
−
{
−
1
,
1
}
. If
det
(
A
2
−
A
)
=
4
\det(A^2 - A) = 4
det
(
A
2
−
A
)
=
4
, then the sum of all possible values of
α
\alpha
α
is equal to (a) 0 (b)
3
2
\frac{3}{2}
2
3
(c)
5
2
\frac{5}{2}
2
5
(d) 2
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