In the oscillation model that describes the user dynamics of online social networks, it is known that the fundamental equation can explicitly describe the causal relationship between the network structure and user dynamics. The fundamental equation uses algebra that satisfies the anti-commutation relation, and its matrix representation is not unique. However, even if the matrix representations are different, the same results should be derived from different representations of the fundamental equation if they are describing the same phenomenon. In this paper, we confirm, using the echo-chamber effect as an example, that the fundamental equations of different matrix representations lead to the same result.