Unipotency of Matrix Group Generated by Two Matrices

In this paper, the problem of unipotency for the matrix group generated by two matrices is examined. By employing matrix logarithms as a tool, various combinatorial formulas for matrices were derived by selecting different primitive elements. Key conclusions were then reached through the organization and simplification of these formulas. It was ultimately demonstrated, based on these conclusions, that a matrix group G generated by two matrices, where the Jordan blocks do not exceed third order, must be unipotent if each primitive element of G is unipotent and has an order of six or less.