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Let $ω \neq 1$ be a cube root of unity and S be the set of all non-singular matrices of the form $A = [\begin{array}{ccc} 1 & a & b \\ ω & 1 & c \\ ω^{2} & ω & 1 \end{array}]$
where $a, b, c$ are either $ω$ or $ω^{2}$ . Then number of distinct matrices in the set S is

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Correct option is A

We have|A|=11cω1−aωcω21+bω1ω2ω=1−cω−aω+acω2=(1−aω)(1−cω)A is non-singular ⇔|A|≠0⇔a=c=ω.Note that b can take any value ω or ω2.Thus, there are two non-singular matrices.

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Let ω≠1 be a cube root of unity and S be the set of all non-singular matrices of the form A=1abω1cω2ω1where a, b, c are either ω or ω2. Then number of distinct matrices in the set S is

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free study material

Let $ω \neq 1$ be a cube root of unity and S be the set of all non-singular matrices of the form $A = [\begin{array}{ccc} 1 & a & b \\ ω & 1 & c \\ ω^{2} & ω & 1 \end{array}]$
where $a, b, c$ are either $ω$ or $ω^{2}$ . Then number of distinct matrices in the set S is