find inverse of the following matrix using elementary operations A = [(2 -6) (1 -2)]
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A=
⎣
⎢
⎢
⎡
1
−1
0
2
3
−2
−2
0
1
⎦
⎥
⎥
⎤
Let A=IA
⇒
⎣
⎢
⎢
⎡
1
−1
0
2
3
−2
−2
0
1
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
1
0
0
0
1
0
0
0
1
⎦
⎥
⎥
⎤
A
[Applying R
2
→R
2
+R
1
]
⇒
⎣
⎢
⎢
⎡
1
0
0
2
5
−2
−2
−2
1
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
1
1
0
0
1
0
0
0
1
⎦
⎥
⎥
⎤
A
[Applying R
1
→R
1
+R
3
, R
2
→R
2
+2R
3
]
⇒
⎣
⎢
⎢
⎡
1
0
0
0
1
−2
−1
0
1
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
1
1
0
0
1
0
1
2
1
⎦
⎥
⎥
⎤
A
[Applying R
3
→R
3
+2R
2
]
⇒
⎣
⎢
⎢
⎡
1
0
0
0
1
0
−1
0
1
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
1
1
2
0
1
2
1
2
5
⎦
⎥
⎥
⎤
A
[Applying R
1
→R
1
+R3]
⇒
⎣
⎢
⎢
⎡
1
0
0
0
1
0
0
0
1
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
3
1
2
2
1
2
6
2
5
⎦
⎥
⎥
⎤
A
Hence, A
−1
=
⎣
⎢
⎢
⎡
3
1
2
2
1
2
6
2
5
⎦
⎥
⎥
⎤
A
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