If ω is a cube root of unity, then find the value of determinant |\table 1+\omega,\omega^2,-\omega;1+\omega^2,\omega,\omega^2;\omega^2+\omega,\omega,\omega|

NIMCET 2013 Question Paper with solutions

Question : 10 of 120

Marks: +1, -0

If ω is a cube root of unity, then find the value of determinant

|\table 1+ω,ω^2,-ω;1+ω^2,ω,ω^2;ω^2+ω,ω,ω|

Solution:

|\table 1+ω,ω^2,-ω;1+ω^2,ω,ω^2;ω^2+ω,ω,ω|=|\table-ω^,ω^2,ω;ω,ω,-ω^2;1,ω,ω-ω^2|

[∵1+ω+ω^2=0]

=ω^2|\table-ω,ω,-1;-1,1,-ω;-1,ω,ω^2|=ω^2|\table0,ω,-1;0,1,-1;ω-1,ω,ω^2|=ω^2×-3=-3ω^2

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