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16.-Linear-Algebra-by-Kenneth-Hoffman
· Problem 5.4.14
Determinants
Mathematics — Linear Algebra · block-matrix-determinant
Problem
Let
A
A
A
,
B
B
B
,
C
C
C
,
D
D
D
be commuting
n
×
n
n \times n
n
×
n
matrices over the field
F
F
F
. Show that the determinant of the
2
n
×
2
n
2n \times 2n
2
n
×
2
n
matrix
[
A
B
C
D
]
\begin{bmatrix} A & B \\ C & D \end{bmatrix}
[
A
C
B
D
]
is
det
(
A
D
−
B
C
)
\det(AD - BC)
det
(
A
D
−
B
C
)
.
Related theory
S Matrix And T Matrix
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