<p>Our paper discusses the abstract algebraic concept of Brandt loopoids, introduced by J. Grabowski. The main result is a generalization of the matrix representation of groupoids over a group to the case of non-associative connected loopoids, where the group component is replaced by a three-parameter family of quasigroups. We establish the conditions under which such matrix loopoids can be constructed and explore examples of connected loopoids that are not groupoids. Particularly interesting cases arise when the quasigroup multiplications are defined by affine maps. In this setting, we provide a general construction of affine loopoids over a two-element set and describe affine loopoids over a three-element set, ensuring that the subloopoids restricted to two elements correspond to the product of the pair groupoid and a group.</p>