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Question
Mathematics
For a invertible matrix A if A ( textadj A )=[10 0 0 10], then | A |=
Q. For a invertible matrix
A
if
A
(
adj
A
)
=
[
10
0
0
10
]
, then
∣
A
∣
=
1625
148
MHT CET
MHT CET 2017
Determinants
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A
100
26%
B
- 100
16%
C
10
53%
D
-10
5%
Solution:
Given :
A
(
adj
A
)
=
[
10
0
0
10
]
=
10
[
1
0
0
1
]
=
10
I
We know that,
A
−
1
=
∣
A
∣
1
Adj
(
A
)
⇒
A
(
adj
A
)
=
∣
A
∣
I
⇒
∣
A
∣
=
10