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Let omega be a complex cube root of unit...

Let `omega` be a complex cube root of unity with `omega!=1a n dP=[p_(i j)]` be a `nxxn` matrix withe `p_(i j)=omega^(i+j)dot` Then `p^2!=O ,w h e nn=` a.`57` b. `55` c. `58` d. `56`

A

`50`

B

`55`

C

`56`

D

`58`

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The correct Answer is:
B, C, D
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Knowledge Check

  • Let omega be a complex cube root of unity with omega ne 0 and P=[p_(ij)] be an n x n matrix with p_(ij)=omega^(i+j) . Then p^2ne0 when n is equal to :

    A
    57
    B
    55
    C
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    D
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  • Let omega be a complex cube root of unity with omegane1 and P = [p_ij] be a n × n matrix with p_(ij) = omega^(i+j) . Then P^2ne0, , when n =

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    57
    B
    55
    C
    58
    D
    56

  • If omega is the cube root of unity, then what is the conjugate of 2omega^2+3i ?

    A
    `2omega-3i`
    B
    `3omega+2i`
    C
    `2omega+3i`
    D
    `3omega-2i`

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