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Question

Let ω be a complex cube root of unity with ω1 and P=[pij] be a n×n matrix with pij=ωi+j. Then, P20 when n=

A
57
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B
55
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C
58
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D
56
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Solution

The correct options are
B 55
C 58
D 56
We know C=A×B=[aik×bkj]
So, P2=[ωi+j×nk=1ω2k]
P2=[ωi+j×ω2×ω2n1w21]
Since P20 every element in the matrix is non-zero
So, ω2n1 should be non-zero 2n must not be a multiple of 3
S0, Option (B),(C) and (D)


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