>[Matrices] seem to represent a more fundamental primordial truth.
No, matrices (or more specifically matrix multiplication) are a useful result picked out of a huge search space defined as "all the ways to combine piles of numbers with arithmetic operators". The utility of the discovery is determined by humans looking for compact ways to represent ideas (abstraction). One of the most interesting anecdotes in the history of linear algebra was how Hamilton finally "discovered" a way to multiply them. "...he was out walking along the Royal Canal in Dublin with his wife when the solution in the form of the equation i2 = j2 = k2 = ijk = −1 occurred to him; Hamilton then carved this equation using his penknife into the side of the nearby Broom Bridge" [0]
The "primordial truth" is found in the selection criteria of the human minds performing the search.