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3
Matrix and determinant
Matrix and determinant
Source:
June 30, 2015
linear algebra
matrix
Problem Statement
Let
A
,
B
∈
M
n
(
C
)
A,B\in M_n(C)
A
,
B
∈
M
n
(
C
)
be two square matrices satisfying
A
2
+
B
2
=
2
A
B
A^2+B^2 = 2AB
A
2
+
B
2
=
2
A
B
.1.Prove that
det
(
A
B
−
B
A
)
=
0
\det(AB-BA)=0
det
(
A
B
−
B
A
)
=
0
. 2.If
r
a
n
k
(
A
−
B
)
=
1
rank(A-B)=1
r
ank
(
A
−
B
)
=
1
, then prove that
A
B
=
B
A
AB=BA
A
B
=
B
A
.
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