# Does this Vandermonde-like matrix always have nonvanishing determinant?


I tried to reduce the matrix to have $$2$$ alphabets with subscripts $$1$$ and $$3$$ alphabets with subscripts $$2$$ to be nonzero, then the determinant would be calculated in a manner very similar to the Vandermonde matrix. But apparently, without making the matrix singular, it seems like only restricted row operations are allowed and this takes me to nowhere.