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Tardigrade
Question
Mathematics
A be a square matrix of order 2 with |A| ≠ 0 such that |A+| A| adj (A)|=0, where adj (A) is a adjoint of matrix A then the value of A-|A| adj (A) mid is
Q.
A
be a square matrix of order 2 with
∣
A
∣
=
0
such that
∣
A
+
∣
A
∣
adj
(
A
)
∣
=
0
,
where adj
(
A
)
is a adjoint of matrix
A
then the value of
A
−
∣
A
∣
adj
(
A
)
∣
is
4014
206
Matrices
Report Error
A
1
B
2
C
3
D
4
Solution:
Let
A
=
[
m
p
n
q
]
, adj
(
a
)
=
[
p
−
p
−
n
m
]
Let
∣
A
∣
=
d
=
m
q
−
n
p
∣
A
+
d
adj
A
∣
=
∣
∣
m
+
q
d
p
(
1
−
d
)
n
(
1
−
d
)
q
+
m
d
∣
∣
=
0
⇒
m
q
+
m
2
d
+
q
2
d
+
m
q
d
2
−
n
p
+
2
n
p
d
−
n
p
d
2
=
0
⇒
(
m
q
−
n
p
)
+
(
m
q
−
n
p
)
d
2
+
m
2
d
+
q
2
d
+
2
m
q
d
−
2
d
2
=
0
⇒
(
d
+
d
3
−
2
d
2
)
+
d
(
m
2
+
q
2
+
2
m
q
)
=
0
⇒
d
[
(
d
−
1
)
2
+
(
m
+
q
)
2
]
=
0
⇒
d
=
1
,
m
+
q
=
0
Now,
∣
A
−
d
adj
∣
A
∣
=
−
(
m
+
q
)
2
+
4
(
m
q
−
n
p
)
=
4
d
=
4