Consider the function
f
:
R
2
→
R
2
f:R
2
→R
2
defined as follows:
f
(
x
,
y
)
=
(
f
1
(
x
,
y
)
,
f
2
(
x
,
y
)
)
f(x,y)=(f
1
(x,y),f
2
(x,y))
where
f
1
(
x
,
y
)
=
x
y
+
y
2
f
1
(x,y)=xy+y
2
and
f
2
(
x
,
y
)
=
x
+
x
y
+
1
f
2
(x,y)=x+xy+1. Define a matrix
A
A as follows:
[
∂
f
1
∂
x
(
4
,
−
3
)
∂
f
1
∂
y
(
4
,
−
3
)
∂
f
2
∂
x
(
4
,
−
3
)
∂
f
2
∂
y
(
4
,
−
3
)
]
∂x
∂f
1
(4,−3)
∂x
∂f
2
(4,−3)
∂y
∂f
1
(4,−3)
∂y
∂f
2
(4,−3)
What will be the determinant of
A
A?
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