A) 0
B) 1
C) 3
D) None of these
Correct Answer: D
Solution :
[d] \[tr(A)=\sum\limits_{i=j}{{{a}_{ij}}}=({{a}_{11}}+{{a}_{22}}+{{a}_{33}}+....+{{a}_{10}})\] \[=({{w}^{2}}+{{w}^{4}}+{{w}^{6}}+....+{{w}^{20}})=\] \[{{w}^{2}}(1+{{w}^{2}}+{{w}^{4}}+...+{{w}^{18}})\] \[={{w}^{2}}[(1+w+{{w}^{2}})+...+(1+w+{{w}^{2}})+1]\] \[={{w}^{2}}\times 1={{w}^{2}}\]
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