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Vojtěch Jarník IMC
2022 VJIMC
2
A^7+A^5+A^3+A=I implies det(A)>0
A^7+A^5+A^3+A=I implies det(A)>0
Source: VJIMC 2022 1.2
April 11, 2022
matrix
linear algebra
Problem Statement
Let
n
≥
1
n\ge1
n
≥
1
. Assume that
A
A
A
is a real
n
×
n
n\times n
n
×
n
matrix which satisfies the equality
A
7
+
A
5
+
A
3
+
A
−
I
=
0.
A^7+A^5+A^3+A-I=0.
A
7
+
A
5
+
A
3
+
A
−
I
=
0.
Show that
det
(
A
)
>
0
\det(A)>0
det
(
A
)
>
0
.
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