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If [1 ω ω²; ω ω² 1; ω² 1 ω] [k 1 1; 1 1 1; 1 1 1] = [0 0 0; 0 0 0; 0 0 0], then the value of k is

1. 6
2. 1
3. 8
4. 9

Correct answer: 1

Solution

Multiplying the two matrices, the only non-zero entries lie in the first column; the (1,1) entry equals k-1, and the other first-column entries also reduce to 0 precisely when k=1. So k=1.

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