Abstract: Firstly, we used the linear transformation of real Clifford algebras to construct the faithful real matrix representations of unit groups of real Clifford algebras Cl*_0,3,Cl*_2,1,Cl*_3,0, and found that they were the subgroups of 8 order real matrix groups. Secondly, we constructed the faithful real matrix representations of real Clifford algebras Cl_2,1 and Cl_3,0 by the relations of basis elements of real Clifford algebras Cl_p,q(p+q=3) and their corresponding matrix relations, we found that they were the subalgebras of 4 order real matrix algebras, and gave their unfaithful real matrix representations.

Key words: unit group, faithful representation, real Clifford algebra, matrix representation