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Problem
Problem
Let matrix
A
=
[
x
y
−
z
1
2
3
1
1
2
]
A = \begin{bmatrix} x & y & -z \\ 1 & 2 & 3 \\ 1 & 1 & 2 \end{bmatrix}
A
=
x
1
1
y
2
1
−
z
3
2
where
x
,
y
,
z
∈
N
x, y, z \in \mathbb{N}
x
,
y
,
z
∈
N
. If
det
(
adj
(
adj
A
)
)
=
2
8
⋅
3
4
\det(\text{adj}(\text{adj } A)) = 2^8 \cdot 3^4
det
(
adj
(
adj
A
))
=
2
8
⋅
3
4
then the number of such matrices
A
A
A
is : [Note :
adj
A
\text{adj } A
adj
A
denotes adjoint of square matrix
A
A
A
.] (a) 220 (b) 45 (c) 55 (d) 110
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