If 3A=(122
21-2
-22-1)then show that A-1 =AT
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Explanation:
3A=
⎣
⎢
⎢
⎡
1
2
x
2
1
2
2
−2
y
⎦
⎥
⎥
⎤
, and AA
′
=I
⇒(3A)(3A
′
)=9I
⇒
⎣
⎢
⎢
⎡
1
2
x
2
1
2
2
−2
y
⎦
⎥
⎥
⎤
⎣
⎢
⎢
⎡
1
2
2
2
1
−2
x
2
y
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
9
0
0
0
9
0
0
0
9
⎦
⎥
⎥
⎤
comparing terms with variables x and y
⇒x+2y=−4 and x−y=−1
solving above equations gives x=−2 and y=−1
∴−x−y=3
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