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IberoAmerican Olympiad For University Students
2005 IberoAmerican Olympiad For University Students
2
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Part of
2005 IberoAmerican Olympiad For University Students
Problems
(1)
A^3=-I, BA^2+BA=C^6+C+I, C symmetric - OIMU 2005 Problem 2
Source:
9/3/2010
Let
A
,
B
,
C
A,B,C
A
,
B
,
C
be real square matrices of order
n
n
n
such that
A
3
=
ā
I
A^3=-I
A
3
=
ā
I
,
B
A
2
+
B
A
=
C
6
+
C
+
I
BA^2+BA=C^6+C+I
B
A
2
+
B
A
=
C
6
+
C
+
I
and
C
C
C
is symmetric. Is it possible that
n
=
2005
n=2005
n
=
2005
?
linear algebra
matrix
algebra
polynomial
linear algebra unsolved