Answer by Gae. S. for Complex equation gives unexpected roots
The condition for invertibility is that $\omega^2ac-(a+c)\omega+1\ne0$. I.e. $(1-\omega a)(1-\omega c)\ne 0$, i.e. $a\ne\omega^2\land c\ne\omega^2$.Which means $2$ matrices.
View ArticleComplex equation gives unexpected roots
The following question requires you to find the number of distinct matrices in S:Let ω≠ 1 be a complex cube root of unity and S be the set of all non singular matrices of the form \begin{bmatrix}...
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