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Mathematics
Problem
Let
A
=
[
a
i
j
]
n
×
n
A = [a_{ij}]_{n \times n}
A
=
[
a
ij
]
n
×
n
be a square matrix and let
c
i
j
c_{ij}
c
ij
be cofactor of
a
i
j
a_{ij}
a
ij
in
A
A
A
. If
C
=
[
c
i
j
]
C = [c_{ij}]
C
=
[
c
ij
]
, then (a)
∣
C
∣
=
∣
A
∣
|C| = |A|
∣
C
∣
=
∣
A
∣
(b)
∣
C
∣
=
∣
A
∣
n
−
1
|C| = |A|^{n-1}
∣
C
∣
=
∣
A
∣
n
−
1
(c)
∣
C
∣
=
∣
A
∣
n
−
2
|C| = |A|^{n-2}
∣
C
∣
=
∣
A
∣
n
−
2
(d) None of these (a)
∣
C
∣
=
∣
A
∣
|C| = |A|
∣
C
∣
=
∣
A
∣
(b)
∣
C
∣
=
∣
A
∣
n
−
1
|C| = |A|^{n-1}
∣
C
∣
=
∣
A
∣
n
−
1
(c)
∣
C
∣
=
∣
A
∣
n
−
2
|C| = |A|^{n-2}
∣
C
∣
=
∣
A
∣
n
−
2
(d) None of these
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