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IMC
1997 IMC
3
I think posted before
I think posted before
Source: IMC 1997 day 1 problem 3
October 1, 2005
linear algebra
linear algebra unsolved
Problem Statement
Let
A
,
B
∈
R
n
×
n
A,B \in \mathbb{R}^{n\times n}
A
,
B
∈
R
n
×
n
with
A
2
+
B
2
=
A
B
A^2+B^2=AB
A
2
+
B
2
=
A
B
. Prove that if
B
A
−
A
B
BA-AB
B
A
−
A
B
is invertible then
3
∣
n
3|n
3∣
n
.
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