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2003 IMC
1
Commuting
Commuting
Source: IMC 2003 day 2 problem 1
October 14, 2005
linear algebra
matrix
linear algebra unsolved
Problem Statement
Let
A
,
B
∈
R
n
×
n
A,B \in \mathbb{R}^{n\times n}
A
,
B
∈
R
n
×
n
such that
A
B
+
B
+
A
=
0
AB+B+A=0
A
B
+
B
+
A
=
0
. Prove that
A
B
=
B
A
AB=BA
A
B
=
B
A
.
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