Addition and multiplication are trivially implemented using lookup, if you had a machine without arithmetic and only control flow and memory operations. You don't need much more than that for matrix operations, and now you have ChatGPT, a decent simulation of apparent thinking - which is all that is necessary to kill the intuition dead.
What is thinking if not a series of matrix operations? Your brain is just a huge network of neurons and their connections, is this not a (very complex) matrix?
Certainly not in any mathematical sense. The discrete N-dimensional coefficients of a matrix are not modeled by neurons, their connections, and the quantum mechanical electrical accidents that (a) constitute one's wetware, and (b) aren't completely captured by gates and code.