It's just all the rings (with 1) I know can be written as a matrix, i.e., find some matrix representation of it (not necessary commutative). Complex numbers for example is written as obvious matrix. E.g. like this
However, is it? possible allowing the matrix to be infinite or just have finite amount of columns.
Like complex numbers are uncountable and it gets around the problem as you can write it as a 2x2 matrix. Even the most exotic example of a ring I know can be written as column finite matrix.
Also, I suppose can all groups be represented as $n \times n$ matrix?