  We introduce a new duality for $\mathcal{N}=1$ supersymmetric gauged matrix
models. This $0d$ duality is an order 4 symmetry, namely an equivalence between
four different theories, hence we call it Quadrality. Our proposal is motivated
by mirror symmetry, but is not restricted to theories with a D-brane
realization and holds for general $\mathcal{N}=1$ matrix models. We present
various checks of the proposal, including the matching of: global symmetries,
anomalies, deformations and the chiral ring. We also consider quivers and the
corresponding quadrality networks. Finally, we initiate the study of matrix
models that arise on the worldvolume of D(-1)-branes probing toric Calabi-Yau
5-folds.
