A proof of An{\dj}eli\'c-Fonseca conjectures on the determinant of some Toeplitz matrices and their generalization

We present a proof of determinant of special nonsymmetric Toeplitz matrices conjectured by An{\dj}eli'c and Fonseca in \cite{andjelic2020some}. A proof is also demonstrated for a more general theorem. The two conjectures are therefore just two possible results, under two specific settings. Numerical examples validating the theorem are provided.