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2011 District Olympiad
3
Romania District Olympiad 2011 - Grade XI
Romania District Olympiad 2011 - Grade XI
Source:
March 12, 2011
linear algebra
linear algebra unsolved
Problem Statement
Let
A
,
B
∈
M
2
(
C
)
A,B\in \mathcal{M}_2(\mathbb{C})
A
,
B
∈
M
2
(
C
)
two non-zero matrices such that
A
B
+
B
A
=
O
2
AB+BA=O_2
A
B
+
B
A
=
O
2
and
det
(
A
+
B
)
=
0
\det(A+B)=0
det
(
A
+
B
)
=
0
. Prove
A
A
A
and
B
B
B
have null traces.
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