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Properties of Determinants

49. Let w≠ 1 ...

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49. Let w≠ 1 be a cube root of unity and S be the set of all non-matrices of the form , where a, b, c are either w or w². Then, the number of distinct matrices in the set S is. 2/6/4/8

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ω \neq 1

be a cube root of unity and S be the set of all non-singular

⎡ ⎢ ⎣ \begin{matrix} 1 & a & b ω & 1 & c ω^{2} & ω & 1 \end{matrix} ⎤ ⎥ ⎦

matrices of the form where each of a,b and c is either

ω

ω^{2}

. Then, the number of distinct matrices in the set S is

w \neq 1

be a cube roots of unity and S be the set of all non-singular matrices of the form

⎡ ⎢ ⎣ \begin{matrix} 1 & a & b ω & 1 & c ω^{2} & ω & 1 \end{matrix} ⎤ ⎥ ⎦

where each a, b and c is either

ω

ω^{2}

. Then the number of district matrices in the set S is?

ω \neq 1

be a cube root of unity and S be the set of all non - singular matrices of the form

⎡ ⎢ ⎣ \begin{matrix} 1 & a & b ω & 1 & c ω^{2} & ω & 1 \end{matrix} ⎤ ⎥ ⎦

, where each of a, b and c is either

ω

ω^{2}

. Then, the number of distinct matrices in the set S is

ω \neq 1

be a cube root of unity and S be the set of all non - singular matrices of the form

⎡ ⎢ ⎣ \begin{matrix} 1 & a & b ω & 1 & c ω^{2} & ω & 1 \end{matrix} ⎤ ⎥ ⎦

, where each of a, b and c is either

ω

ω^{2}

. Then, the number of distinct matrices in the set S is

ω \neq 1

be a cube root of unity and

S

be the set of all non-singular matrices of the form

⎡ ⎢ ⎣ \begin{matrix} 1 & a & b ω & 1 & c ω^{2} & ω & 1 \end{matrix} ⎤ ⎥ ⎦

a, b

c

ω

ω^{2}

. Then the number of distinct matrices in the set

S

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