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Army Group X Practice Set 4
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© examsnet.com
Question : 58
Total: 70
If
ω
is the cube root of unity, then
|
I
ω
ω
2
ω
ω
2
I
ω
2
I
ω
|
=
?
1
ω
ω
2
0
Validate
Solution:
Let A=
|
I
ω
ω
2
ω
ω
2
I
ω
2
I
ω
|
=
|
1
+
ω
+
ω
2
ω
ω
2
1
+
ω
+
ω
2
ω
2
1
1
+
ω
+
ω
2
1
ω
|
[
by
C
1
→
C
1
+
C
2
+
C
3
]
=
(
1
+
ω
+
ω
2
)
|
1
ω
ω
2
1
ω
2
1
1
1
ω
|
[by
(
1
+
ω
+
ω
2
)
common from
C
1
]
=
0
×
|
1
ω
ω
2
1
ω
2
1
1
1
ω
|
by
[
∵
1
+
ω
+
ω
2
=
0
]
=
0
© examsnet.com
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