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VTRMC
2009 VTRMC
Problem 5
3x3 matrices in C
3x3 matrices in C
Source: VTRMC 2009 P5
May 31, 2021
matrix
linear algebra
Problem Statement
Suppose
A
,
B
∈
M
3
(
C
)
A,B\in M_3(\mathbb C)
A
,
B
∈
M
3
(
C
)
,
B
≠
0
B\ne0
B
=
0
, and
A
B
=
0
AB=0
A
B
=
0
. Prove that there exists
D
∈
M
3
(
C
)
D\in M_3(\mathbb C)
D
∈
M
3
(
C
)
with
D
≠
0
D\ne0
D
=
0
such that
A
D
=
D
A
=
0
AD=DA=0
A
D
=
D
A
=
0
.
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