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AP EAMCET Engineering 2018 Apr 22 Shift 1 Paper
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© examsnet.com
Question : 4
Total: 160
For the matrix
A
=
[
3
−
3
4
2
−
3
4
0
−
1
1
]
,
A
−
1
=
A
A
2
A
3
A
4
Validate
Solution:
The determinant of A comes out to be,
|
A
|
=
[
3
−
3
4
2
−
3
4
0
−
1
1
]
|
A
|
=
3
(
−
3
+
4
)
+
3
(
2
)
+
4
(
−
2
)
=
1
≠
0
Taking the adjacent of
A
we get.
adj
(
A
)
=
[
1
−
2
−
2
−
2
3
3
0
−
4
−
3
]
=
[
1
−
1
0
−
2
3
−
4
−
2
3
−
3
]
A
−
1
=
adj
(
A
)
|
A
|
=
[
1
−
1
0
−
2
3
−
4
−
2
3
−
3
]
On squaring the given determinant.
A
2
=
A
.
A
=
[
3
−
3
4
2
−
3
4
0
−
1
1
]
[
3
−
3
4
2
−
3
4
0
−
1
1
]
A
2
=
[
3
−
4
4
0
−
1
0
−
2
2
−
3
]
A
3
=
[
3
−
4
4
0
−
1
0
−
2
2
−
3
]
[
3
−
3
4
2
−
3
4
0
−
1
1
]
=
[
1
−
1
0
−
2
3
−
4
−
2
3
−
3
]
Thus, the inverse of
A
comes out to be
A
−
1
=
A
3
.
© examsnet.com
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