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1997 IMC
2
Det of block matrix (trivial)
Det of block matrix (trivial)
Source: IMC 1997 day 2 problem 2
October 19, 2005
linear algebra
matrix
linear algebra unsolved
Problem Statement
Let
M
∈
G
L
2
n
(
K
)
M \in GL_{2n}(K)
M
∈
G
L
2
n
(
K
)
, represented in block form as
M
=
[
A
B
C
D
]
,
M
−
1
=
[
E
F
G
H
]
M = \left[ \begin{array}{cc} A & B \\ C & D \end{array} \right] , M^{-1} = \left[ \begin{array}{cc} E & F \\ G & H \end{array} \right]
M
=
[
A
C
B
D
]
,
M
−
1
=
[
E
G
F
H
]
Show that
det
M
.
det
H
=
det
A
\det M.\det H=\det A
det
M
.
det
H
=
det
A
.
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